Waves & Sound

Example:
Ocean wave travels toward shore, but water particles just move up and down — they don't travel across the ocean!

Wavelength (λ): Distance from one crest to next crest (or trough to trough)

Frequency (f): Number of waves passing a point per second (Hz)

Amplitude (A): Maximum displacement from rest position

Crest: Highest point of wave

Trough: Lowest point of wave

Wavefront: The line marking the "edge" of a wave spreading outward

Transverse: Particles oscillate perpendicular to wave direction

Examples: light, radio waves, water waves, string vibrations

Longitudinal: Particles oscillate parallel to wave direction (compressions & rarefactions)

Examples: sound waves, ultrasound, seismic P-waves

where: v = wave speed (m/s), f = frequency (Hz), λ = wavelength (m)

Rearrangements:

f = v / λ | λ = v / f

Key insight: If speed is constant, higher frequency = shorter wavelength

Question:
A sound wave has frequency 440 Hz and speed 330 m/s (in air). Find wavelength.

Solution:

v = fλ

Rearrange: λ = v / f

λ = 330 / 440

Waves bounce off surfaces

Real examples:

Light reflects off mirror

Sound reflects in cave (echo), in concert halls

Water waves reflect off cliff face

Refraction: Wave changes direction when it enters a new medium (speed changes)

Examples:

Light slows in glass → bends (refraction)

Sound travels faster in water than air → bends at boundary

Straw in water appears bent (light refraction)

Diffraction: Wave spreads out when passing through a gap or around an obstacle

Real-world examples:

Radio waves diffract around buildings (λ is long)

Light doesn't diffract noticeably (λ is tiny)

Sound diffracts around corners (λ ≈ cm to m)

Observations:

✓ Can measure wavelength (distance between crests)

✓ Can observe reflection (waves bounce off solid barrier)

✓ Can observe refraction (waves bend entering shallow water)

✓ Can observe diffraction (waves spread through gap)

Produced by: Vibrating objects (vocal cords, tuning fork, speaker cone)

Detected by: Ear drum vibrates, sends signals to brain

Compression/rarefaction: Molecules oscillate parallel to wave direction, creating pressure variations

Sound CANNOT travel in vacuum

Speed of sound varies by medium:

Air (20°C): ≈ 330-350 m/s

Water: ≈ 1500 m/s (faster — denser)

Steel: ≈ 5000 m/s (fastest — very dense)

Human ear hears: 20 Hz (lowest) to 20,000 Hz = 20 kHz (highest)

Below 20 Hz: Infrasound (not heard, but felt as vibration)

Above 20 kHz: Ultrasound (not heard by humans, used by animals & technology)

Amplitude ↔ Loudness: Larger amplitude = louder sound

Frequency ↔ Pitch: Higher frequency = higher pitch

Measuring speed of sound experiment:

1. Clap two blocks together (create sound)

2. Measure distance to echo (canyon or cliff)

3. Measure time to hear echo

4. Distance = 2 × measured distance ÷ 2 (echo travels there and back)

5. Speed = distance / time

Echo: Sound reflects off a surface (wall, canyon, building)

Minimum distance for echo:
v = 330 m/s, time = 0.1 s
Distance = 330 × 0.1 = 33 m (round trip: wall is ≈ 16.5 m away)

Applications: Sonar, medical ultrasound (uses echoes to image)

Definition: Sound with frequency above human hearing (> 20,000 Hz)

Real-world uses (IGCSE syllabus):

✓ Medical imaging (ultrasound scan of pregnancy)

✓ Sonar: Submarines/ships detect objects by ultrasound echoes

✓ Testing: Industrial ultrasound to detect cracks in metal

✓ Cleaning: Ultrasonic waves vibrate dirt off objects

Question:
A submarine sends ultrasound pulse. Echo returns after 0.4 seconds. Sound speed in seawater = 1500 m/s. How far is the object?

Solution:

Distance traveled by sound = speed × time = 1500 × 0.4 = 600 m

This is the round trip (there and back)

✅ Waves transfer energy, not matter

✅ v = fλ (wave speed equation)

✅ Transverse: oscillation perpendicular (light, water)

✅ Longitudinal: oscillation parallel (sound, compressions/rarefactions)

✅ Reflection: angle of incidence = angle of reflection

✅ Refraction: direction changes entering new medium

✅ Diffraction: spreads through gap or around obstacle

✅ Ripple tank demonstrates all three (reflection, refraction, diffraction)

✅ Sound is longitudinal (compressions & rarefactions)

✅ Requires medium (no sound in vacuum)

✅ Audible range: 20 Hz to 20 kHz (humans)

✅ Speed: ~330 m/s air, ~1500 m/s water, ~5000 m/s steel

✅ Amplitude ↔ loudness | Frequency ↔ pitch

✅ Ultrasound (> 20 kHz): medical, sonar, testing

✅ Echoes: reflected sound (used in sonar)

✅ Waves transfer energy without transferring matter

✅ v = fλ — fundamental wave equation

✅ Transverse vs longitudinal — know the difference

✅ Reflection, refraction, diffraction — all testable in ripple tank

✅ Sound is longitudinal with compressions/rarefactions

✅ Audible 20 Hz–20 kHz; ultrasound > 20 kHz

✅ Sound speed: solids > liquids > gases

✅ Ultrasound uses: medical, sonar, testing

Waves & sound — vibrations everywhere! 🌊