Hey Tara! Welcome to the world of Waves and Light. This is one of the most beautiful topics in physics -- you experience waves every single day without even realising it. Every time you hear the horn of a BMTC bus, see the ripples when rain falls into a puddle on Brigade Road, or watch the shimmer of light off Ulsoor Lake, you are seeing waves in action. This guide will take you through everything step by step, with lots of Indian examples to help it all click. You have got this!
What Are Waves?
Imagine you are sitting at Cubbon Park and you throw a stone into the lake. Ripples spread out from where the stone lands, moving outward in circles. Now here is the key insight: the water itself does not travel outward. If you placed a small leaf floating on the water, it would bob up and down as the wave passes, but it would not be carried to the edge of the lake. The wave moves outward, but the water stays roughly where it is.
This is the fundamental idea behind all waves:
Waves transfer energy without transferring matter. This is one of the most tested definitions in the entire IGCSE course. Memorise it word for word. The examiner loves to test whether you understand that the medium (water, air, rope) vibrates but does not actually travel with the wave.
Think about doing a "Mexican wave" at an IPL cricket match at M. Chinnaswamy Stadium. Each person stands up and sits down (they vibrate in place), and the wave pattern moves around the stadium. But no person actually runs around the stadium! The wave carries energy (it takes effort to stand up), but no matter (no person) is transferred from one end to the other.
Waves can travel through different media:
- Ropes and strings -- flick one end of a skipping rope and watch a wave pulse travel to the other end. The rope vibrates but the fibres do not move along it.
- Springs (Slinky) -- push and pull a Slinky and you can see compression waves travel along it. The coils vibrate but stay in roughly the same position.
- Water -- waves on a lake, the ocean, or even in your chai cup when you tap the side. The water particles move in small circles but the wave energy spreads outward.
- Air -- sound waves travel through air. When an auto-rickshaw honks, the air molecules vibrate back and forth, passing the sound energy to your ear, but the air itself does not fly from the auto to you.
Wave Features -- The Key Terms
To describe waves precisely, we need specific vocabulary. Let us go through each term carefully.
Wavefront
A wavefront is a line joining all the points on a wave that are at the same phase (same point in their vibration cycle). Think of the circular ripples spreading out when you drop a stone in water -- each ring is a wavefront. For waves approaching a beach, the wavefronts are roughly straight lines parallel to the shore.
Crest and Trough
A crest is the highest point of the wave -- the peak. A trough is the lowest point -- the dip. If you watch waves at Marina Beach or any Indian coastline, the crests are the tops of the waves where surfers ride, and the troughs are the valleys between them.
Amplitude
The amplitude is the maximum displacement of a wave from its rest position (the undisturbed, equilibrium position). It is measured from the rest position to the crest (or from the rest position to the trough) -- NOT from crest to trough.
A very common mistake is measuring amplitude from crest to trough. That distance is actually twice the amplitude. If the distance from crest to trough is 8 cm, the amplitude is 4 cm. Always measure from the rest position (the middle line) to the crest OR trough.
Amplitude tells you how much energy a wave carries. A gentle ripple in your chai has a small amplitude; a tsunami has a massive amplitude carrying devastating energy.
Wavelength (λ)
The wavelength is the distance between two consecutive points that are in phase -- for example, the distance from one crest to the next crest, or one trough to the next trough. We use the Greek letter lambda (λ) to represent it, measured in metres (m).
λ looks like a wave! The Greek letter lambda (λ) actually looks like a tiny wave with a peak -- perfect for remembering it represents wavelength.
Frequency (f)
The frequency is the number of complete waves passing a point per second. It is measured in hertz (Hz), where 1 Hz = 1 wave per second.
Think about it this way: if you stand on a bridge over a canal and count how many wave crests pass under you in one second, that number is the frequency. If 5 crests pass every second, the frequency is 5 Hz.
Wave Speed (v)
The wave speed is how fast the wave pattern moves through the medium, measured in metres per second (m/s). This is NOT the speed of the particles vibrating -- it is the speed at which the energy travels.
All of these quantities are connected by one of the most important equations in wave physics:
"Very Fine Lamb" -- v = f × λ. Think of a very fine lamb grazing peacefully in the Nilgiri Hills. V for Very, F for Fine, λ (lambda / Lamb) for wavelength. Or use the triangle: put v on top, f and λ on the bottom. Cover what you want to find!
v = 3.0 × 10⁸ m/s
Always convert units before substituting into v = f × λ. If frequency is given in kHz, convert to Hz (multiply by 1000). If in MHz, multiply by 10⁶. The examiner gives units like kHz or MHz to test whether you can convert correctly.
Transverse Waves
In a transverse wave, the vibration of the particles is perpendicular (at right angles) to the direction the wave travels.
Imagine shaking a rope side-to-side while your friend holds the other end. Your hand moves up and down, but the wave pulse travels horizontally along the rope. The vibration (up-down) is perpendicular to the wave direction (horizontal). That is a transverse wave.
Important examples of transverse waves:
- Water surface waves -- the water moves up and down while the wave moves horizontally across the surface
- All electromagnetic (EM) radiation -- light, radio waves, microwaves, X-rays, UV, infrared, gamma rays. These are ALL transverse waves
- S-waves (secondary seismic waves) -- these travel through the Earth during an earthquake. India sits on the Indo-Australian tectonic plate, so understanding seismic waves matters! S-waves can only travel through solids, which is how scientists discovered the Earth's outer core is liquid
- Waves on ropes and strings -- like the strings of a sitar or veena vibrating
"S for Side-to-side and Secondary" -- S-waves are transverse because the particles move Side-to-side (perpendicular) to the wave direction. Also, S-waves arrive Second at a seismometer (after P-waves), just like "S" comes after "P" in the alphabet.
Longitudinal Waves
In a longitudinal wave, the vibration of the particles is parallel to (along the same direction as) the direction the wave travels.
Imagine pushing and pulling one end of a Slinky spring. The coils bunch together (compressions) and spread apart (rarefactions) as the wave travels along. The coils vibrate back-and-forth in the same direction the wave moves. That is a longitudinal wave.
Instead of crests and troughs, longitudinal waves have:
- Compressions -- regions where particles are squashed close together (like a traffic jam on Silk Board junction!)
- Rarefactions -- regions where particles are spread far apart (like the empty road at 4 AM)
Important examples of longitudinal waves:
- Sound waves -- when you speak, your vocal cords vibrate and push air molecules back and forth, creating compressions and rarefactions that travel to the listener's ear
- P-waves (primary seismic waves) -- these are the fastest seismic waves and arrive first at seismometers. They can travel through solids AND liquids, which is why they pass through the Earth's liquid outer core
- Compression waves in springs -- pushing and pulling a Slinky
How to tell them apart in the exam: The key question is "which direction do the particles vibrate relative to the wave direction?" If perpendicular → transverse. If parallel → longitudinal. Sound is ALWAYS longitudinal. Light is ALWAYS transverse. These are the two that come up most often.
Wave Behaviours: Reflection, Refraction, and Diffraction
All waves -- whether water, sound, or light -- show three key behaviours. Understanding these is essential for your exam.
Reflection
Reflection occurs when a wave hits a surface and bounces back. Think of an echo -- when you shout near a large building (like the walls of Bangalore Fort), the sound wave bounces off the wall and comes back to you. Water waves in a ripple tank bounce off a straight barrier in the same way.
The wave keeps the same speed, wavelength, and frequency after reflection. Only the direction changes.
Refraction
Refraction occurs when a wave changes speed as it passes from one medium to another (or from one depth to another), causing it to change direction.
Think about waves approaching a beach at an angle. Where the water becomes shallower, the waves slow down and bend so they arrive almost parallel to the shore. In a ripple tank, when water waves pass from a deep region to a shallow region, they slow down and the wavelength decreases. If they enter at an angle, they change direction.
Key point: the frequency stays the same during refraction (it depends on the source, not the medium), but the speed and wavelength change.
Diffraction
Diffraction is the spreading out of waves when they pass through a gap or around an edge.
You experience diffraction every day! When you are standing outside a classroom and can hear the teacher speaking even though you cannot see them through the doorway, that is because sound waves diffract (spread out) as they pass through the door opening. Sound has a long wavelength, so it diffracts a lot around everyday obstacles.
In a ripple tank, you can observe all three behaviours:
- Reflection -- place a straight barrier in the tank and waves bounce off it
- Refraction -- place a glass plate under part of the tank to make the water shallower. Waves slow down and change direction when they cross from deep to shallow water
- Diffraction through a gap -- place two barriers with a gap between them. Waves spread out after passing through the gap
- Diffraction at an edge -- place a single barrier. Waves bend around the edge of the barrier into the "shadow" region
When drawing diffraction diagrams, the wavelength must stay the SAME on both sides of the gap. Many students draw the waves with a different spacing after the gap -- this loses marks. Also, the waves spread out in a circular pattern from the gap, and they curve around the edges.
How Wavelength and Gap Size Affect Diffraction
The amount of diffraction depends on the relationship between the wavelength and the size of the gap:
- When the gap is much larger than the wavelength, there is very little diffraction -- the waves pass straight through with only slight bending at the edges
- When the gap is about the same size as the wavelength, maximum diffraction occurs -- the waves spread out in a wide semicircular pattern
- When the gap is smaller than the wavelength, very little wave energy passes through
This is why you can hear someone talking around a corner (sound wavelength is about 0.3-3 m, similar to doorway width) but you cannot see them around the corner (light wavelength is about 500 nm = 0.0000005 m, far smaller than any doorway).
Diffraction at an Edge
When waves meet an edge (rather than a gap), they bend around it. Longer wavelengths diffract more around the edge than shorter wavelengths. This is why you can hear low-pitched sounds (long wavelength) from behind a wall more easily than high-pitched sounds (short wavelength).
For maximum marks on diffraction questions, state that "most diffraction occurs when the gap width is approximately equal to the wavelength." At an edge, state that "longer wavelengths diffract more than shorter wavelengths."
Ripple tank experiments are a favourite in Paper 6 (practical). Know that: (1) a lamp above the tank projects wave patterns onto a white screen below, (2) you use a stroboscope to "freeze" the wave pattern, and (3) the depth of water controls the wave speed (shallower = slower).
Time for P-waves: t = 150,000 / 6000 = 25 s.
Time for S-waves: t = 150,000 / 3500 = 42.9 s.
Difference = 42.9 - 25 = 17.9 seconds.
The P-waves arrive about 18 seconds before the S-waves.
As the wave enters shallow water, it slows down (the wave speed decreases). But the wave's energy stays roughly the same. Since the energy is related to the amplitude, and the wave is being compressed into a smaller space, the amplitude must increase. The wave "piles up" into a taller wall of water.
λ = v / f = (3 x 10⁸) / (98.3 x 10⁶) = 3.05 m.
The wavelength is about 3 metres, which is comparable to the size of gaps between buildings. When a wave encounters a gap that is roughly equal to its wavelength, maximum diffraction occurs -- the wave spreads out around the obstacle. That is why FM radio waves can bend around buildings to reach you.
4 complete waves in 0.040 s, so period T = 0.040 / 4 = 0.010 s.
Frequency f = 1 / T = 1 / 0.010 = 100 Hz.
When the drummer hit harder, the trace got taller -- the amplitude increased. The frequency stayed the same (same number of waves in the same time). Greater amplitude means a louder sound with more energy, but the pitch (frequency) is unchanged.
3.2.1 Reflection of Light
When light hits a smooth surface like a mirror, it bounces back. This is reflection. You use this every morning when you look in a mirror to get ready for school!
Key Terms for Reflection
- Normal -- an imaginary line drawn at right angles (90°) to the mirror surface at the point where the light ray hits. This is your reference line for measuring angles
- Angle of incidence (i) -- the angle between the incoming (incident) ray and the normal
- Angle of reflection (r) -- the angle between the reflected ray and the normal
Angles are ALWAYS measured from the normal, not from the mirror surface. This is a very common mistake. If the question says "a ray hits a mirror at 30° to the surface," then the angle of incidence is actually 90° - 30° = 60° (measured from the normal).
The Law of Reflection
This law works every single time, without exception. Whether it is a bathroom mirror, the rear-view mirror of an auto-rickshaw, or a lake reflecting the sunset -- the angle of incidence always equals the angle of reflection.
Images in a Plane Mirror
When you look in a flat (plane) mirror, you see an image of yourself. This image has specific properties that the examiner loves to test:
- Same size as the object
- Same distance behind the mirror as the object is in front
- Virtual -- the image cannot be projected onto a screen. The light rays do not actually come from behind the mirror; your brain just interprets them as if they do
- Laterally inverted -- left and right are swapped. This is why the word "AMBULANCE" is written backwards on the front of Indian ambulances, so it reads correctly in your rear-view mirror!
"SALT" for plane mirror image properties: Same size, As far behind the mirror, Laterally inverted, The image is virtual. Remember: "The mirror gives you SALT -- Same size, As far behind, Laterally inverted, and it is a virTual image."
Constructing Mirror Images
For the extended syllabus, you need to be able to draw accurate ray diagrams showing how a plane mirror forms an image:
- Draw the mirror as a straight line with hatching on the back
- Place the object in front of the mirror
- Draw the normal at the point where each ray hits the mirror
- Draw the reflected ray so that the angle of reflection equals the angle of incidence
- Extend the reflected rays backwards (as dotted lines) behind the mirror -- they meet at the image position
- The image is the same distance behind the mirror as the object is in front
You can also use calculations: if an object is 25 cm in front of a plane mirror, the image is exactly 25 cm behind the mirror. The total distance from object to image is 50 cm.
3.2.2 Refraction of Light
Have you ever noticed that a spoon in a glass of chai looks bent at the surface of the liquid? Or that the bottom of a swimming pool always looks shallower than it actually is? That is refraction -- the bending of light when it passes from one transparent material to another.
Why Does Light Bend?
Light travels at different speeds in different materials. In a vacuum, light travels at its maximum speed (3 × 10⁸ m/s). In glass, it slows down to about 2 × 10⁸ m/s. In water, it is about 2.25 × 10⁸ m/s. When light changes speed at a boundary, it changes direction (unless it hits the boundary at exactly 90°).
Key Terms for Refraction
- Normal -- a line at right angles to the boundary surface at the point where the light enters
- Angle of incidence (i) -- the angle between the incident ray and the normal
- Angle of refraction (r) -- the angle between the refracted ray and the normal
The Rules of Refraction
When light goes from a less dense material to a more dense material (e.g., air → glass):
- Light slows down
- Light bends towards the normal
- Angle of refraction is smaller than the angle of incidence
When light goes from a more dense material to a less dense material (e.g., glass → air):
- Light speeds up
- Light bends away from the normal
- Angle of refraction is larger than the angle of incidence
"FAST medium = FAT angle" -- In the faster (less dense) medium, the angle from the normal is bigger (fatter). In the slower (more dense) medium, the angle is smaller (thinner). Think of it like Bangalore traffic: on the narrow, crowded MG Road (dense medium), you move slowly and stay close to the centre line (small angle from normal). On the open Mysore Expressway (less dense), you spread out and move fast (large angle from normal).
Experiment: Refraction by a Transparent Block
In this classic experiment, you shine a ray of light into a rectangular glass or Perspex block:
- The ray bends towards the normal when entering the block (air → glass, slowing down)
- The ray travels straight through the block
- The ray bends away from the normal when leaving the block (glass → air, speeding up)
- The emerging ray is parallel to the incident ray but shifted sideways (laterally displaced)
When drawing refraction through a rectangular block, the emergent ray MUST be parallel to the incident ray. If your diagram shows them at different angles, something is wrong. Also, if light hits the boundary along the normal (at 0°), it passes straight through without bending.
Critical Angle and Total Internal Reflection
When light travels from a denser medium to a less dense medium (like glass to air), something special can happen:
- At small angles of incidence: some light is refracted (bends away from the normal) and some is reflected back inside. This is partial internal reflection
- At the critical angle (c): the refracted ray travels exactly along the boundary surface (angle of refraction = 90°). This is the tipping point
- At angles greater than the critical angle: no light escapes -- ALL of it is reflected back inside the denser medium. This is total internal reflection (TIR)
The critical angle is the angle of incidence in the denser medium for which the angle of refraction is exactly 90°.
For total internal reflection to occur, TWO conditions must be met: (1) light must be travelling from a denser medium to a less dense medium (e.g., glass to air, NOT air to glass), and (2) the angle of incidence must be greater than the critical angle. Many students forget condition 1!
Refractive Index (n)
The refractive index of a material tells you how much it slows down light compared to a vacuum (or air, which is almost the same). It is defined as the ratio of speeds:
Typical values: glass ≈ 1.5, water ≈ 1.33, diamond ≈ 2.42, air ≈ 1.0.
Snell's Law
sin r = sin i / n
r = sin⁻¹(0.4714) = 28.1°
Refractive Index and Critical Angle
This formula connects the refractive index directly to the critical angle. A higher refractive index means a smaller critical angle (so TIR happens more easily). Diamond has n = 2.42, so its critical angle is only about 24° -- this is why diamonds sparkle so brilliantly! Most light that enters gets trapped inside and bounces around before escaping.
c = sin⁻¹(0.6667) = 41.8°
Optical Fibres
Total internal reflection is the principle behind optical fibres -- the thin glass or plastic cables that carry internet data all across India and the world. When Tara streams a video on her phone, that data likely travels thousands of kilometres through optical fibres under the Indian Ocean (like the submarine cables connecting India to Singapore and Europe).
How they work: a light signal enters one end of the fibre. The fibre is so thin that light always hits the inner surface at an angle greater than the critical angle, so it undergoes total internal reflection again and again, bouncing along the length of the fibre without escaping. The light (carrying data) can travel enormous distances with very little energy loss.
Advantages of optical fibres over copper cables:
- Much higher data capacity (bandwidth)
- No electrical interference
- Thinner and lighter
- More secure (harder to tap)
- Signals travel further before needing amplification
3.2.3 Thin Lenses
Lenses are pieces of transparent material (usually glass or plastic) with curved surfaces. They are everywhere in your daily life -- in your eyes, in cameras, in your spectacles (if you wear them), in the projector at school, and in magnifying glasses.
Two Types of Lenses
Converging lens (convex lens) -- thicker in the middle than at the edges. When a parallel beam of light passes through it, the rays are brought together (converge) to meet at a single point called the principal focus (F).
Diverging lens (concave lens) -- thinner in the middle than at the edges. When a parallel beam of light passes through it, the rays spread out (diverge) as if they came from a point behind the lens. This point is also called the principal focus, but it is virtual (on the same side as the incoming light).
Think of Caves: A conCAVE lens has a "cave" shape (thinner in the middle, like a cave entrance) and light diverges. A conVEX lens bulges outward (like a pregnant belly) and brings light together. Also: "con-VEX = con-VERGE" -- they both start with "conv"!
Key Lens Terms
- Principal axis -- the straight line passing through the centre of the lens, perpendicular to the lens surface
- Principal focus (F) -- the point where parallel rays converge (for a converging lens) or appear to diverge from (for a diverging lens)
- Focal length (f) -- the distance from the centre of the lens to the principal focus. A fat, strongly curved lens has a short focal length; a thin, gently curved lens has a long focal length
Ray Diagrams for Converging Lenses -- Real Images
To find where an image forms, you draw at least two of these three standard rays:
- Parallel ray -- arrives parallel to the principal axis, then refracts through the principal focus F on the other side
- Central ray -- passes straight through the centre of the lens without bending
- Focal ray -- passes through the principal focus F on the near side, then refracts to emerge parallel to the principal axis
Where two rays cross on the other side of the lens, that is where the real image forms. A real image can be projected onto a screen (like a cinema screen or the retina of your eye).
Image Characteristics
An image can be described using three properties:
- Size -- magnified (bigger), diminished (smaller), or same size
- Orientation -- upright (same way up as the object) or inverted (upside down)
- Type -- real (can be projected on a screen) or virtual (cannot be projected)
For a converging lens, when the object is beyond the principal focus (more than one focal length away), the image is real and inverted. The further the object is from the lens, the smaller the image becomes.
Virtual Images
When an object is placed between F and the lens (closer than one focal length), the rays diverge after passing through the lens. Your eye traces these diverging rays back to where they appear to meet -- behind the object, on the same side of the lens. This creates a virtual image that is upright, magnified, and on the same side as the object.
A diverging lens always produces a virtual image that is upright, diminished (smaller), and on the same side as the object, no matter where the object is placed.
When drawing ray diagrams: (1) always use a ruler, (2) draw at least TWO rays from the top of the object, (3) use solid lines for real rays and dashed lines for virtual rays (extensions behind the lens), (4) mark the image clearly with an arrow. Sloppy diagrams lose marks!
Ray Diagram for Virtual Image (Converging Lens)
When the object is between F and the lens:
- Draw a ray parallel to the principal axis -- it refracts through F on the far side
- Draw a ray through the centre of the lens -- it passes straight through
- These two refracted rays diverge on the far side. Extend them backwards (dashed lines) to the near side where they appear to meet
- That meeting point is where the virtual, upright, magnified image forms
Magnifying Glass
A single converging lens used as a magnifying glass works by placing the object closer than the focal length. The lens produces a virtual, upright, magnified image that you see when you look through the lens. Every shopkeeper at KR Market checking the quality of spices with a magnifying glass is using this principle!
Correcting Vision Defects
Short-sightedness (myopia) -- the eyeball is too long, or the eye lens is too strong, so distant objects are focused in front of the retina. Corrected with a diverging (concave) lens, which spreads out the light before it enters the eye, moving the focal point back onto the retina.
Long-sightedness (hypermetropia) -- the eyeball is too short, or the eye lens is too weak, so close objects are focused behind the retina. Corrected with a converging (convex) lens, which brings the light together more before it enters the eye, moving the focal point forward onto the retina.
"Short sight needs a Short lens name" -- Short-sighted people need a diverging (concave) lens. "concave" has fewer letters than "converging" -- short name for short sight! Alternatively: "My DIVe" -- Myopia is corrected with a DIVerging lens.
3.2.4 Dispersion of Light
White light looks, well, white. But it is actually a mixture of many different colours of light. When white light passes through a glass prism, it splits into a beautiful band of colours called a spectrum. This splitting is called dispersion.
Why Does Dispersion Happen?
Different colours of light have slightly different speeds in glass. Red light is the fastest and bends the least; violet light is the slowest and bends the most. Because each colour refracts by a slightly different amount at both surfaces of the prism, they separate into a spectrum.
The Seven Colours (in order)
From least bent to most bent (or from longest wavelength to shortest):
Red -- Orange -- Yellow -- Green -- Blue -- Indigo -- Violet
"VIBGYOR" -- Every Indian student knows this! Read the colours backwards (from violet to red): Violet, Indigo, Blue, Green, Yellow, Orange, Red. Or in order from red: "ROY G. BIV" is the English version. Or try: "Richard Of York Gave Battle In Vain".
You see dispersion in nature when sunlight passes through raindrops and creates a rainbow! The raindrop acts like a tiny prism, splitting the white sunlight into its component colours. Bangalore gets some spectacular rainbows during the monsoon season.
In the exam, when asked about dispersion through a prism, always state that red is deviated (bent) the least and violet is deviated the most. If drawing a diagram, red must be on the outer edge (least bent) and violet on the inner edge (most bent) of the emerging spectrum.
Monochromatic Light
Monochromatic light means light of a single frequency (and therefore a single colour and single wavelength). "Mono" means one, "chromatic" means colour.
A laser produces monochromatic light. A sodium street lamp produces nearly monochromatic yellow light. If you pass monochromatic light through a prism, it does NOT split into a spectrum -- it just bends (refracts) as a single colour because there is only one frequency present.
White light is the opposite of monochromatic -- it is polychromatic, containing a mixture of all visible frequencies.
If asked "what is monochromatic light?", the precise answer is "light of a single frequency." Do NOT say "single colour" -- while technically similar, the syllabus definition specifically uses "frequency." A laser is the best example of a monochromatic source.
Each time the light enters a less dense layer, it bends away from the normal (just like light going from glass to air). Eventually the angle of incidence exceeds the critical angle, and total internal reflection occurs -- the light reflects back upward toward your eyes.
Your brain assumes light travels in straight lines, so it thinks the light came from the ground. You see an image of the sky on the road -- which looks like water.
Since 24.4 degrees is very small, most light rays that enter the diamond bounce around inside it multiple times before finally escaping through the top face. Each bounce redirects the light, creating intense flashes of brilliance.
Glass imitation (critical angle ~42 degrees) lets much more light escape through the sides and bottom, so fewer internal reflections occur and the stone looks dull in comparison.
We can verify: sin c = 1/n, so sin c = 1/2.42 = 0.413, and c = sin⁻¹(0.413) = 24.4 degrees. ✔
Your brain traces the light rays back in straight lines and thinks the tiles are at a shallower position than they really are.
Refractive index n = real depth / apparent depth = 2.0 m / 1.5 m = 1.33.
This matches the known refractive index of water (1.33). ✔
Each image is formed further behind its respective mirror. The images alternate between being laterally inverted and not (Image 1 is inverted, Image 2 is not, Image 3 is inverted again...). Each successive image appears dimmer because some light is absorbed at each reflection.
All images are virtual -- they cannot be projected onto a screen because the light rays only appear to come from behind the mirror. They never actually pass through the image position.
The fibre is designed so that light hits the boundary at an angle greater than the critical angle. This means 100% of the light is reflected back into the core -- none escapes into the cladding. The light zigzags along the entire length of the fibre.
Without cladding, the light would hit a glass-air boundary. While TIR could still occur, any scratches, dirt, or contact with another fibre would disrupt the reflection. The cladding provides a controlled, clean boundary with a precise critical angle, ensuring reliable TIR even when the cable is bent or bundled with other fibres.
What is the Electromagnetic Spectrum?
Tara, you already use the electromagnetic spectrum every single day -- you just might not know it by that name! When you watch a YouTube video on your phone, your phone receives microwaves from a cell tower. When you change the TV channel with a remote, you are using infrared. When you step out into the Bangalore sunshine, visible light and ultraviolet radiation hit your skin. All of these are electromagnetic (EM) waves.
Here is the key idea: all EM waves are transverse waves that can travel through a vacuum (empty space). They do not need a medium. That is how sunlight reaches Earth across 150 million km of empty space. Pretty amazing, right?
The entire family of EM waves is arranged in a continuous band called the electromagnetic spectrum. They are all the same type of wave -- the only difference is their wavelength and frequency.
All EM waves travel at the same speed in a vacuum. This is the speed of light. Do not say "light travels fastest" -- ALL EM waves travel at exactly the same speed in vacuum. The difference between them is wavelength and frequency, NOT speed.
The EM Spectrum in Order
You must know the seven main regions of the spectrum. Here they are, arranged from longest wavelength / lowest frequency to shortest wavelength / highest frequency:
Running Man In Very Ugly Xtra-large Green shorts = Radio, Microwaves, Infrared, Visible, Ultraviolet, X-rays, Gamma rays. This goes from longest wavelength to shortest. Imagine this runner jogging around Cubbon Park -- unforgettable!
An important relationship to remember:
- As wavelength decreases, frequency increases (they are inversely related)
- As frequency increases, the wave carries more energy
- So gamma rays (shortest wavelength, highest frequency) are the most energetic and most dangerous
- Radio waves (longest wavelength, lowest frequency) are the least energetic and least dangerous
Speed of EM Waves in Vacuum
All electromagnetic waves travel at the same speed in a vacuum:
This speed is often called the speed of light, but remember that ALL EM waves -- not just visible light -- travel at this speed in a vacuum. The wave equation still applies:
v = c = 3.0 × 10⁸ m/s
λ = 3.05 m
v = c = 3.0 × 10⁸ m/s
f = 2.46 × 10⁹ Hz
f ≈ 2.46 GHz
v = c = 3.0 × 10⁸ m/s
λ = 1.0 × 10⁻¹⁰ m
λ = 0.1 nm
When using the wave equation with EM waves, always check your units! Convert wavelengths to metres (not cm or nm) before putting them into the equation. The most common mistake is forgetting to convert MHz to Hz (multiply by 10⁶) or cm to m (divide by 100).
Uses of Each Type of EM Wave
This is a really important section for your exam, Tara. You need to know the typical uses for each region of the spectrum. Let us go through them one by one with examples you will recognise from daily life in Bangalore.
(a) Radio Waves -- longest wavelength, lowest frequency
- Radio and TV broadcasting -- Radio Mirchi 98.3, Red FM, All India Radio all send radio waves to your receiver. Doordarshan uses radio waves for TV transmission too.
- Astronomy -- Radio telescopes pick up radio waves from distant stars and galaxies. India's Giant Metrewave Radio Telescope (GMRT) near Pune is one of the world's largest!
- RFID (Radio-Frequency Identification) -- The FASTag on your family's car uses RFID to automatically pay tolls on the NICE Road or Bangalore-Mysore Expressway. Metro smart cards also use RFID.
(b) Microwaves
- Satellite TV -- Tata Sky, Airtel Digital TV, and Dish TV all receive signals via microwaves beamed from satellites
- Mobile phones -- When you make a call or use 4G/5G data on Jio or Airtel, your phone communicates with the cell tower using microwaves
- Microwave ovens -- The microwave oven in your kitchen heats food by making water molecules vibrate very fast
(c) Infrared (IR)
- Grills and heaters -- The tandoor at your favourite restaurant uses infrared radiation to cook naan and tikka
- Remote controls -- Your TV remote sends IR signals (try pointing it at your phone camera -- you can actually see the IR flash!)
- Intruder alarms / motion sensors -- Security systems in shops on MG Road or Commercial Street detect the IR emitted by a person's warm body
- Thermal imaging -- Remember during COVID, thermal cameras at Bangalore airport checked passengers' temperatures? Those detect infrared radiation
- Optical fibres -- Your Jio Fiber or ACT Fibernet broadband uses infrared light travelling through glass fibres to deliver super-fast internet
(d) Visible Light
- Vision -- The only part of the EM spectrum your eyes can detect! The seven colours of the rainbow: Red, Orange, Yellow, Green, Blue, Indigo, Violet (ROYGBIV)
- Photography -- Your phone camera captures visible light to take photos
- Illumination -- LED bulbs, tube lights, and the beautiful Lalbagh flower show lights all produce visible light
(e) Ultraviolet (UV)
- Security marking -- Invisible ink that only shows up under UV light is used on concert tickets and exam papers to prevent counterfeiting
- Detecting fake bank notes -- Banks use UV lamps to check if a ₹500 or ₹2000 note is genuine. Real notes have special UV-reactive markings
- Sterilising water -- UV water purifiers (like Kent or Aquaguard) use UV light to kill bacteria and viruses in drinking water. Very common in Indian homes!
(f) X-rays
- Medical scanning -- When you break a bone playing basketball or fall off a bicycle, the doctor takes an X-ray because X-rays pass through soft tissue but are absorbed by bones, creating a shadow image
- Security scanning -- Baggage scanners at Namma Metro stations and Bangalore airport use X-rays to see inside your bags without opening them
(g) Gamma Rays -- shortest wavelength, highest frequency, most energetic
- Sterilising food and medical equipment -- Gamma rays kill bacteria on surgical instruments and can preserve packaged food without heating it
- Cancer detection (imaging) -- Doctors inject a gamma-emitting tracer into the patient and use a special camera to detect cancer cells
- Cancer treatment (radiotherapy) -- Focused beams of gamma rays are aimed at tumours to destroy cancer cells. Major cancer hospitals in Bangalore like Kidwai Memorial use this
For remembering uses, think of them in terms of what you encounter in a typical day: Wake up and listen to Radio Mirchi. Call Amma on your Microwave-using mobile. She is cooking with the Infrared tandoor. You See (visible light) the food. Apply UV sunscreen before going out. Get an X-ray at the hospital. Gamma rays treat the illness.
Harmful Effects of EM Radiation
The higher the frequency (and energy) of an EM wave, the more damage it can do to your body. Here are the dangers you need to know:
| EM Wave | Harmful Effect | Why? |
|---|---|---|
| Microwaves | Internal heating of body tissue | Microwaves can penetrate skin and heat water in your cells, like a microwave oven heats food |
| Infrared | Skin burns | Too much IR causes burns -- like standing too close to a bonfire during Bhogi / Lohri |
| Ultraviolet | Skin cancer, eye damage | UV damages DNA in skin cells (causing cancer) and can damage the cornea and retina of your eyes |
| X-rays | Cell mutation and damage | X-rays can ionise atoms in your cells, damaging DNA and potentially causing cancer with excessive exposure |
| Gamma rays | Cell mutation and damage | Most penetrating and energetic -- causes the most severe cell damage. That is why radiographers stand behind lead shields |
Notice the pattern: radio waves and visible light are NOT listed as harmful in the syllabus. The harmful effects start from microwaves and get progressively worse as frequency increases. Also note that X-rays and gamma rays cause the SAME type of harm (cell mutation/damage) -- the exam sometimes tests whether you know both cause the same thing.
Satellite Communication Using Microwaves
When you watch a cricket match on Star Sports via Tata Sky, the signal travels from the stadium to a satellite in space and back down to your dish antenna -- all using microwaves. Let us understand how this works.
(a) Low Earth Orbit Satellites
- Orbit at heights of about 200-2000 km above Earth
- They move across the sky quickly (they orbit the Earth in about 90 minutes)
- Because they are close, signals are stronger and need less power
- Used for weather monitoring, imaging, and some phone networks
- You need many satellites to maintain continuous coverage because each one is only overhead for a short time
- Example: India's ISRO launches many low orbit satellites -- CartoSat for mapping, OceanSat for weather
(b) Geostationary Satellites
- Orbit at a height of about 36,000 km above the equator
- They orbit at exactly the same rate as the Earth rotates, so they appear to stay fixed above one spot
- Your satellite dish can point at one fixed position in the sky and always receive the signal
- Used for TV broadcasting (Tata Sky, Dish TV), weather (INSAT), and long-distance communication
- Being much further away means signals are weaker and there is a small time delay
A classic exam question is: "Why do satellite TV dishes not need to track the satellite across the sky?" The answer is that TV satellites are geostationary -- they orbit above the equator at the same rate Earth spins, so they stay in the same position relative to the ground. The dish only needs to be pointed once.
Communication Systems
This extended section covers three important communication technologies you use every day:
(a) Mobile Phones Use Microwaves
Why microwaves and not radio waves? Two reasons:
- Microwaves can penetrate walls and buildings -- so your Jio or Airtel signal works inside your house, inside a classroom, even inside Mantri Mall
- Microwave wavelengths are short enough for a short aerial -- the antenna inside your phone is tiny. If phones used radio waves, you would need an antenna several metres long! Imagine walking around with a 3-metre antenna sticking out of your phone.
(b) Bluetooth Uses Radio Waves
When you connect your wireless earbuds or share files between phones using Bluetooth:
- Bluetooth uses short-range radio waves
- Radio waves can pass through walls -- so your Bluetooth speaker works from the next room
- Bluetooth is designed for short distances (typically up to 10 m)
(c) Optical Fibres Use Visible Light or Infrared
Your ACT Fibernet or Jio Fiber uses optical fibres -- thin glass strands that carry light signals:
- Visible light or infrared travels along the fibre by total internal reflection
- Optical fibres achieve extremely high data rates -- that is why fibre broadband is so much faster than 4G
- They can carry far more information than radio waves or microwaves
Think of it as a speed ranking: Mobile = Microwaves (both start with M!), Bluetooth = radio waves (B for Both-rooms, because radio passes through walls), Fibre = light/infrared (F for Fastest!).
Digital vs Analogue Signals
Signals can be sent in two ways:
| Feature | Analogue Signal | Digital Signal |
|---|---|---|
| What it looks like | A smooth, continuous wave that varies in amplitude and frequency | A series of ON/OFF pulses (only two values: 0 or 1) |
| Example | Old AM radio, vinyl records, old telephone landlines | Digital TV (Tata Sky), 4G/5G mobile data, MP3 music files |
| Effect of noise | Noise distorts the signal and cannot be removed | Noise can be identified and removed -- signal regenerated cleanly |
Sound as digital or analogue: When you speak, your voice creates an analogue sound wave (a continuous wave). But when you record a song on your phone or send a voice note on WhatsApp, your phone converts it to a digital signal (a series of 0s and 1s). The phone samples the analogue wave many times per second and stores each sample as a number.
Benefits of Digital Signals Over Analogue
- Increased data rate -- digital signals can carry much more information per second. That is why 4G streaming works better than old FM radio for music
- Increased range -- digital signals can travel further because they can be regenerated (cleaned up) at relay stations without losing quality
- Accurate regeneration -- this is the big one. When an analogue signal picks up noise (static, interference), the noise becomes part of the signal and you cannot remove it. But with digital, since the signal is just 0s and 1s, a relay station can read the noisy signal, figure out whether each pulse was meant to be a 0 or a 1, and regenerate a perfect clean copy. It is like photocopying a photocopy versus retyping a text message -- the retyped version stays perfect.
The key word for digital signal advantage is "regeneration" not "amplification". Analogue signals can be amplified too, but amplification makes the noise louder as well. Digital signals can be regenerated -- meaning the noise is stripped away and a clean signal is created. Use the word "regenerated" in your exam answer for full marks.
Different materials absorb different amounts of X-rays. Dense metals absorb more (appear darker/blue), while organic materials absorb less (appear lighter/orange). This creates a contrast image of the bag contents.
The same penetrating ability that makes X-rays useful also makes them dangerous: they can penetrate human tissue and damage or kill living cells. This can cause mutations leading to cancer. That is why the scanner has lead-lined walls (lead absorbs X-rays) and the operator sits behind a protective screen.
Time = distance / speed = 2.25 x 10¹¹ / 3 x 10⁸ = 750 seconds = 12.5 minutes.
So when ISRO sends a command from Bangalore, it takes 12.5 minutes to reach Mangalyaan, and 12.5 minutes for the response to come back -- a 25-minute round trip.
Radio waves are used because they have the longest wavelength in the EM spectrum, which means they diffract the most around obstacles and can spread out over large distances. They also pass through Earth's atmosphere with minimal absorption, unlike infrared or UV which get absorbed by gases in the atmosphere.
The microwave wavelength is 12.2 cm, but the holes in the mesh are only about 1 mm (0.1 cm) across. The holes are much smaller than the wavelength, so the microwaves cannot pass through -- they are reflected by the metal mesh.
Visible light has a wavelength of about 400-700 nm (0.0004-0.0007 mm), which is thousands of times smaller than the 1 mm holes. The holes are much larger than the wavelength of visible light, so light passes straight through without significant diffraction. You can see your food, but the microwaves stay inside.
UV-C sits just beyond the violet end of the visible spectrum -- it has a shorter wavelength and higher frequency than visible light. Higher frequency means higher energy per photon.
This higher energy is enough to break chemical bonds in DNA molecules, killing bacteria and viruses. Visible light has lower energy photons that cannot break these bonds -- the light passes through or is absorbed without causing significant damage to DNA.
This is also why UV from the sun causes sunburn -- it damages skin cell DNA. UV-C is the most energetic type of UV and is the most effective at sterilisation.
Gamma rays: frequency ≈ 10₂⁰ Hz, wavelength ≈ 10⁻¹² m
Infrared: frequency ≈ 10¹² Hz, wavelength ≈ 10⁻⁴ m
Gamma rays have a frequency about 100 million times higher than infrared. Since energy is proportional to frequency, each gamma ray photon carries enormously more energy than an infrared photon.
This energy is enough to ionise atoms (knock electrons off), break molecular bonds, and destroy DNA -- killing bacteria. Infrared photons only have enough energy to make molecules vibrate (causing heating), which is why your remote control is harmless and why infrared is used in heaters, but gamma rays require thick lead or concrete shielding.
Practice Questions -- 3.3 Electromagnetic Spectrum
How is Sound Produced?
Tara, sound is everywhere around you in Bangalore -- the honking of auto-rickshaws on MG Road, the announcements on the Namma Metro, your favourite songs playing on Spotify, the school bell, your teacher's voice. But where does all this sound come from?
Here is the fundamental rule: sound is produced by vibrating sources. No vibration = no sound. Every single sound you have ever heard was made by something vibrating.
- When you speak, your vocal cords vibrate
- When a cricket bat hits a ball, the bat vibrates (that satisfying "crack" sound!)
- A tabla produces sound because the membrane vibrates when the musician strikes it
- A guitar string vibrates when plucked
- A loudspeaker has a cone that vibrates back and forth
- Even a honking auto-rickshaw has a vibrating diaphragm inside its horn
You can feel these vibrations! Touch your throat while humming -- you will feel the vibrations of your vocal cords. Touch a speaker playing loud music and you can feel it shaking.
If an exam question asks "How is sound produced?", always use the word "vibrating" or "vibrations" in your answer. Simply saying "by hitting something" is NOT enough. Say: "Sound is produced when an object vibrates, causing the air particles around it to vibrate."
Sound is a Longitudinal Wave
This is a crucial point, Tara. Sound is a longitudinal wave. What does this mean?
In a longitudinal wave, the vibrations of the particles are parallel to (along the same direction as) the direction the wave travels. Think of it this way:
Imagine you are standing in a packed BMTC bus during rush hour. Everyone is squished together. Now the bus brakes suddenly. What happens? The person at the front gets pushed forward, bumps into the person ahead, and a wave of pushing travels through the bus from back to front. The people are moving forward and backward (the same direction the wave moves) -- that is a longitudinal wave!
This is exactly how sound travels through air:
- A vibrating object (say, a loudspeaker cone) pushes the air particles in front of it forward
- These air particles bump into the particles next to them, pushing them forward
- This creates a chain reaction -- a wave of pushes travelling outward from the source
- The air particles themselves do not travel far -- they just vibrate back and forth around their normal position
Compressions and Rarefactions
When a longitudinal sound wave passes through air, it creates two alternating regions:
Think of the BMTC bus analogy again:
Compression = a region where air particles are pushed close together (high pressure). It is like when the bus brakes and everyone at the front is squished together -- bodies pressed tight, no space between people.
Rarefaction = a region where air particles are spread far apart (low pressure). It is like when the bus accelerates again and the people at the back suddenly have too much space -- gaps open up between everyone.
A sound wave is a series of compressions and rarefactions travelling outward from the vibrating source, like ripples spreading out -- except instead of going up and down (like water waves), the air particles push back and forth.
Compression = Crowded (particles close together, like the crowd in a packed BMTC bus at Majestic). Rarefaction = Room (particles have room to spread out, like an empty bus at midnight). Both start with the same letter!
The Audible Range of Human Hearing
Humans can only hear sounds within a certain range of frequencies:
Some fun facts:
- A bass guitar produces sounds as low as about 40 Hz
- The lowest note on a tabla is around 50-80 Hz
- A normal conversation is around 300-3000 Hz
- A cricket's chirping (the insect, not the sport!) can be around 3000-8000 Hz
- Dogs can hear up to about 45,000 Hz -- that is why a dog whistle works even though you cannot hear it
- Bats can hear up to 100,000 Hz and use ultrasound for navigation
- As people get older, they lose the ability to hear higher frequencies. Your parents probably cannot hear sounds above 15,000 Hz that you can!
Sound Needs a Medium
This is one of the biggest differences between sound and electromagnetic waves. Sound cannot travel through a vacuum. It MUST have a medium (solid, liquid, or gas) to travel through.
Why? Because sound works by particles bumping into each other. In a vacuum, there are no particles, so there is nothing to bump. It is like trying to pass a message in a game of Chinese Whispers (telephone game) with no people in the chain -- impossible!
That is why in space, which is mostly a vacuum, there is complete silence. In sci-fi movies when spaceships explode with a big "BOOM" -- that is actually wrong! There would be no sound at all in the vacuum of space.
The classic experiment to demonstrate this uses a bell jar:
- Place an electric bell inside a glass bell jar
- Switch on the bell -- you can hear it ringing
- Use a vacuum pump to remove the air from the bell jar
- As air is removed, the sound gets quieter and quieter
- When most of the air is removed, you can see the bell vibrating but you can barely hear it
- You cannot get a perfect vacuum in a school lab, but the demonstration clearly shows that removing the medium reduces the sound
Be careful: do NOT say "you hear nothing" in the bell jar experiment. In a school lab, you cannot achieve a perfect vacuum, so you would still hear a very faint sound. Say "the sound becomes very faint" or "almost inaudible" rather than "the sound disappears completely".
Speed of Sound in Different Media
Sound travels at different speeds in different materials. The key rule is:
Sound is fastest in solids > faster in liquids > slowest in gases
Why? In solids, particles are closest together and have the strongest forces between them, so vibrations pass quickly from one particle to the next. Think of it like a line of people standing shoulder to shoulder passing a nudge along -- it travels really fast because there is no gap. In gases, particles are far apart, so each one has to travel further before bumping into the next one -- like people standing far apart in a line, the nudge takes longer to travel.
| Medium | Approximate Speed | Example |
|---|---|---|
| Air (gas) | ~330-350 m/s | Normal sound around you |
| Water (liquid) | ~1500 m/s | Sound underwater in a swimming pool |
| Steel (solid) | ~6000 m/s | Sound travelling along railway tracks |
This is why you can hear an approaching Indian Railways train by putting your ear to the steel rail long before you can hear it through the air! The sound travels through the solid steel much faster than through the air. (Please do NOT actually try this on a real railway track -- it is extremely dangerous!)
Speed of Sound in Air
For comparison, this is about:
- About 1,224 km/h (faster than any car, but slower than a passenger aircraft)
- About 1 km every 3 seconds -- this is useful for estimating how far away a thunderstorm is!
Thunder trick: During Bangalore's monsoon thunderstorms, count the seconds between seeing the lightning and hearing the thunder. Divide by 3 to get the distance in km. See lightning, count "1...2...3...4...5...6" then hear thunder? That is 6 ÷ 3 = 2 km away. This works because light is almost instant (3 × 10⁸ m/s) while sound takes about 3 seconds per km.
Experiment: Measuring the Speed of Sound
The IGCSE exam often asks about this experiment. Here is a simple method:
Method 1: Two observers with a large distance
- Measure a large distance (at least 100 m) between two points -- you could do this on your school's cricket ground or running track
- One person at point A claps two wooden blocks together (or bangs a drum)
- A second person at point B starts a stopwatch when they see the clap and stops it when they hear the clap
- This works because light travels almost instantly, but sound takes a noticeable time
- Repeat several times and take an average to reduce random errors
- Calculate: speed = distance / time
t = 0.44 s
v = 341 m/s
Common exam improvements for this experiment: (1) Use a larger distance to make the time interval bigger and easier to measure accurately. (2) Repeat and average to reduce random errors from reaction time. (3) Use an electronic timer with microphones at each end instead of a stopwatch to remove human reaction time completely.
Amplitude, Loudness, Frequency, and Pitch
Two important relationships you need to know:
| Wave Property | What You Hear | Example |
|---|---|---|
| Amplitude (height of wave) | Loudness | A drummer hitting the tabla harder makes a louder sound (bigger amplitude). Whispering vs shouting. |
| Frequency (vibrations per second) | Pitch | A veena's thin string vibrates fast = high frequency = high pitch. The thick string vibrates slowly = low frequency = low pitch. |
- Bigger amplitude = louder sound (more energy). Think of the difference between tapping a tabla gently vs hitting it hard
- Higher frequency = higher pitch. Think of a baby's cry (high pitch, high frequency) vs a man's deep voice (low pitch, low frequency)
- These are independent -- you can have a loud, low-pitched sound (like a bass drum) or a quiet, high-pitched sound (like a whistle far away)
Amplitude = Awaz (volume/loudness in Hindi). Frequency = how Fast the pitch goes (higher frequency = higher pitch). Two simple letter associations!
Echo: Reflection of Sound
An echo is simply the reflection of sound. When you shout "HELLO!" towards a large building or cliff, you hear "HELLO!" coming back to you a moment later. That is an echo.
How it works:
- You produce a sound (shout)
- The sound wave travels through the air towards a large, hard surface (a wall, building, cliff)
- The sound wave reflects off the surface
- The reflected wave travels back to your ears
- You hear the original sound again -- that is the echo
For an echo to be heard distinctly, the reflecting surface needs to be at least about 17 metres away. This is because your ears need about 0.1 seconds between the original sound and the echo to hear them as separate sounds. At 340 m/s, sound travels 34 m in 0.1 s, but it has to go there AND back (34 / 2 = 17 m).
Try this: stand in front of a large building (like a wall of your school or a big apartment complex) and clap. If you are far enough away, you will hear the clap echo back!
Echo questions often involve calculating distances. Remember that the sound travels to the reflecting surface AND back again, so the total distance = 2 × distance to the wall. A very common mistake is forgetting to divide by 2!
Ultrasound
Ultrasound is any sound with a frequency greater than 20,000 Hz (20 kHz) -- above the upper limit of human hearing. You cannot hear ultrasound, but it has many useful applications.
Uses of Ultrasound
1. Non-Destructive Testing (Checking for cracks)
Ultrasound pulses are sent into metal structures like bridge supports, railway tracks, or aircraft parts. If there is a crack inside the metal, the ultrasound reflects off the crack and comes back early. By analysing the reflections, engineers can find hidden defects without cutting the metal open. Indian Railways uses this to check for cracks in rails!
2. Medical Scanning (Ultrasound imaging)
This is the most well-known use. Ultrasound is used to create images of babies in the womb (prenatal scans). It is also used to examine kidneys, the liver, and other internal organs. Ultrasound is preferred over X-rays for this because:
- It is safe -- no ionising radiation, so it does not damage cells
- It can show soft tissue clearly (X-rays are better for bones)
- It can create real-time moving images
3. Sonar (Sound Navigation and Ranging)
Ships and submarines use sonar to measure ocean depth or find objects underwater. A pulse of ultrasound is sent downward, it reflects off the seabed (or a submarine, or a school of fish), and the echo returns. The time taken for the echo to return tells you the distance.
The Indian Navy uses sonar extensively for submarine detection, and fishing boats in coastal Karnataka use it to locate fish!
t = 0.4 s
d = 600 / 2
d = 300 m
t = 3.2 s
d = 4800 / 2
d = 2400 m
d = 2.4 km
t = 0.00012 s
d = 0.72 / 2
d = 0.36 m
The Wave Equation Applied to Sound
The wave equation works for sound waves too:
v = 340 m/s
When a question asks "Can a human hear this sound?" -- you need to check TWO things: (1) Is the frequency between 20 Hz and 20,000 Hz? (2) Is the sound travelling through a medium (not a vacuum)? Both conditions must be met for a human to hear the sound.
For the d = vt/2 sonar equation, think: "Sound goes on a RETURN trip". Like an auto-rickshaw going to the market and coming back -- the total distance on the meter is double the actual distance to the market. So you divide by 2 to get the one-way distance.
Light travels at 3 x 10⁸ m/s, so the flash takes 680 / (3 x 10⁸) = 0.0000023 seconds to reach you -- essentially instant.
Sound travels at only 340 m/s, so the boom takes 680 / 340 = 2 seconds to reach you.
You see the flash before hearing the boom because light travels approximately 1 million times faster than sound. The light arrives almost instantly while the sound takes a noticeable time to cover the same distance.
When she presses the fret, the vibrating length L gets shorter, so the wavelength λ also gets shorter.
The wave speed v on the string depends on the string's tension and thickness, which have not changed. Since v = f x λ, and v is constant but λ has decreased, the frequency f must increase.
Higher frequency = higher pitch. That is why the second note sounds higher.
For example, if the full string length is 90 cm and she halves it to 45 cm: the wavelength halves, so the frequency doubles -- producing a note one octave higher.
But the sound went down to the fish and back up, so: depth = 120 / 2 = 60 m.
Ultrasound (frequency above 20 kHz) is used instead of audible sound because:
1. It can be formed into a narrow, focused beam (less spreading), giving a more precise location
2. It does not disturb the fish or the crew (humans cannot hear it)
3. It has short wavelengths which reflect well off small objects like fish
This would not work well in air because the speed of sound in air is only 340 m/s (much slower) and, more importantly, ultrasound is heavily absorbed by air over short distances. Water is a much better medium for transmitting sound over long distances because the molecules are closer together.
This tiny wavelength means the ultrasound can detect details as small as about 0.44 mm, giving a detailed image of the baby.
Ultrasound is used instead of X-rays because:
1. X-rays are ionising radiation -- they can damage the baby's developing cells and DNA, potentially causing mutations or birth defects
2. Ultrasound is non-ionising -- it is just high-frequency sound waves that reflect off boundaries between different tissues. It causes no known harm to the mother or baby
Audible sound (20 Hz - 20 kHz) would not work because it has much longer wavelengths (e.g., at 20 kHz: λ = 1540/20000 = 0.077 m = 7.7 cm). This wavelength is far too large to detect the fine details of a developing baby -- you need a wavelength comparable to or smaller than the features you want to image.
Time = (2 x 85) / 340 = 170 / 340 = 0.5 seconds. This is greater than 0.1 s, so you hear a distinct echo. ✔
Echo from the farther building (170 m away):
Time = (2 x 170) / 340 = 340 / 340 = 1.0 second. This is also greater than 0.1 s, so you hear this echo too. ✔
The two echoes arrive at different times (0.5 s and 1.0 s), so you will hear two separate, distinct echoes -- the first from the closer building, then the second from the farther building 0.5 seconds later.
If you were only 10 m from a wall: time = (2 x 10) / 340 = 0.059 s. This is less than 0.1 s -- you would NOT hear a distinct echo. The reflected sound would merge with the original sound (this is called reverberation).