Waves & Sound
Waves are disturbances that transfer energy without transferring matter. Sound is a mechanical longitudinal wave that travels through solids, liquids, and gases.
This guide covers wave types, sound properties, the wave equation, worked examples, and memory aids to help you truly understand — not just memorize — waves and sound.
1What Are Waves?
A wave is a disturbance that transfers energy from one point to another without transferring matter. The medium (particles) vibrate about their rest position, but they do not travel with the wave.
Waves are everywhere — from ocean waves and earthquakes to light and sound. Understanding wave behaviour is essential for physics, engineering, and even music.
Shake one end of a rope up and down. A wave travels along the rope to the other end — but the rope itself doesn't move forward. The wave carries energy, not matter.
Waves transfer energy, not matter. The particles of the medium vibrate in place — they do not travel with the wave.
Transverse Wave
Sound example: When you speak, air particles vibrate back and forth near their original positions. The vibration pattern (sound wave) travels from your mouth to someone's ear — but the air particles themselves do not travel across the room.
2Key Definitions
Wave
A disturbance that transfers energy from one point to another without transferring matter.
Mechanical Wave
A wave that requires a medium (solid, liquid, or gas) to travel through. Sound is a mechanical wave.
Transverse Wave
A wave where particles vibrate perpendicular (at right angles) to the direction of wave travel. Example: water waves, light.
Longitudinal Wave
A wave where particles vibrate parallel (back and forth) to the direction of wave travel. Example: sound waves.
Wavelength (λ)
The distance between two consecutive identical points on a wave (e.g. crest to crest). Measured in metres (m).
Frequency (f)
The number of complete waves passing a point per second. Measured in Hertz (Hz).
Amplitude (A)
The maximum displacement of a particle from its rest position. Related to the energy/loudness of the wave.
Wave Speed (v)
The speed at which a wave travels through a medium. Measured in metres per second (m/s).
Compression
A region in a longitudinal wave where particles are pushed close together (high pressure).
Rarefaction
A region in a longitudinal wave where particles are spread far apart (low pressure).
3Types of Waves
Waves are classified by the direction of particle vibration relative to the direction of wave travel. The two main types are transverse and longitudinal waves.
Transverse Waves
Particles vibrate perpendicular (at right angles) to the direction of wave travel.
- Water waves (surface)
- Light waves
- Waves on a rope or string
Vibration is perpendicular to wave direction
Longitudinal Waves
Particles vibrate parallel (back and forth) to the direction of wave travel.
- Sound waves
- Pressure waves
- Seismic P-waves
Vibration is parallel to wave direction
Longitudinal Wave
"Transverse = T = Top-to-bottom vibration. Longitudinal = L = Left-to-right vibration."
4Sound Waves
Sound is a mechanical longitudinal wave. It is produced when an object vibrates, creating a series of compressions (high pressure) and rarefactions (low pressure) in the surrounding medium.
Sound cannot travel through a vacuum. It requires a medium (air, water, steel, etc.) because it needs particles to vibrate.
Speed of Sound in Different Media
Sound travels at different speeds depending on the medium. Particles that are closer together and more tightly bonded transmit vibrations faster.
Solids
Fastest
~5000 m/s (steel)
Liquids
Medium speed
~1500 m/s (water)
Gases
Slowest
~340 m/s (air)
Pitch and Volume
Two key properties of sound are pitch and volume. They are determined by different wave characteristics and are completely independent of each other.
Higher Frequency
= Higher Pitch
e.g. a whistle, soprano voice
Greater Amplitude
= Louder Sound
e.g. shouting vs whispering
Interactive: Wave Properties
Adjust frequency and amplitude to see how the wave changes. Watch how wavelength responds.
v = fλ → 3 × 113.3 = 340 m/s
Think of a guitar string. A tighter, thinner string vibrates faster (higher frequency) and produces a higher-pitched note. Plucking harder (greater amplitude) makes it louder, but doesn't change the pitch.
5The Wave Equation
The wave equation connects speed, frequency, and wavelength. This is the single most important formula for wave calculations.
v = fλ
v = wave speed (metres per second, m/s)
f = frequency (Hertz, Hz)
λ = wavelength (metres, m)
Speed of sound in air ≈ 340 m/s
This value is commonly used in exam questions unless another speed is specified.
You can rearrange v = fλ to find any unknown: f = v / λ or λ = v / f. Always check your units before calculating.
6Worked Examples
Example 1: Find the wave speed
A sound wave has a frequency of 500 Hz and a wavelength of 0.68 m. Calculate the wave speed.
v = fλ
v = 500 × 0.68
v = 340 m/s
Example 2: Find the wavelength
Sound travels at 340 m/s in air. If the frequency is 256 Hz, what is the wavelength?
λ = v / f
λ = 340 / 256
λ = 1.33 m
Example 3: Find the frequency
A sound wave in water has a speed of 1500 m/s and a wavelength of 3 m. What is the frequency?
f = v / λ
f = 1500 / 3
f = 500 Hz
Example 4: How long for sound to travel a distance?
How long does it take for sound to travel 680 m in air (speed of sound = 340 m/s)?
v = d / t, so t = d / v
t = 680 / 340
t = 2 s
7Memory Aids
"Very Fast Waves" — v = fλ
The initials V, F, W match the formula: velocity (speed) = frequency × wavelength.
"High frequency, high pitch"
The faster a wave vibrates (higher frequency), the higher the pitch you hear. Think of a whistle compared to a bass drum.
"Big amplitude, big sound"
Greater amplitude means more energy, which means a louder sound. Shouting produces bigger vibrations than whispering.
8Common Mistakes
Confusing frequency with amplitude
Frequency determines pitch (how high or low a sound is). Amplitude determines loudness (how loud or quiet). They are completely independent properties — changing one does not affect the other.
Forgetting units in calculations
Always include units: frequency in Hz, wavelength in m, and speed in m/s. Forgetting to convert (e.g. using cm instead of m) leads to answers that are off by factors of 100 or more.
Assuming sound can travel through a vacuum
Sound is a mechanical wave that requires a medium. In a vacuum (like outer space), there are no particles to vibrate, so sound cannot travel. This is a very common exam mistake.
Mixing up transverse and longitudinal waves
In transverse waves, particles vibrate perpendicular to wave direction (like shaking a rope). In longitudinal waves, particles vibrate parallel to wave direction (like a slinky pushed back and forth). Sound is longitudinal, not transverse.
9Quick Revision Summary
- ✓Waves transfer energy, not matter.
- ✓Sound is a longitudinal mechanical wave — it needs a medium to travel.
- ✓Transverse waves: particles vibrate perpendicular to wave direction (e.g. water waves).
- ✓Longitudinal waves: particles vibrate parallel to wave direction (e.g. sound).
- ✓The wave equation: v = fλ (speed = frequency × wavelength).
- ✓Speed of sound in air ≈ 340 m/s.
- ✓Sound travels fastest in solids, slowest in gases.
- ✓Higher frequency = higher pitch. Greater amplitude = louder sound.
Frequently Asked Questions
- Can sound travel through space?
- No. Sound is a mechanical wave that needs a medium. Space is a near-vacuum with no particles to vibrate. Light (electromagnetic) can travel through space, but sound cannot.
- Why does sound travel faster in solids than gases?
- Particles in solids are closer together and more tightly bonded, so vibrations pass between them more quickly. In gases, particles are spread far apart and collide less frequently.
- What is the Doppler effect?
- When a sound source moves toward you, the waves are compressed (higher frequency/pitch). When it moves away, the waves stretch out (lower frequency/pitch). This is why a siren sounds higher as an ambulance approaches.
- What is an echo?
- An echo is a reflected sound wave. When sound hits a hard surface (like a cliff), it bounces back. You hear it as a separate sound if the surface is far enough away (at least ~17 m) for the delay to be noticeable.
- What is the difference between pitch and volume?
- Pitch is determined by frequency (how fast the wave vibrates). Volume (loudness) is determined by amplitude (how big the vibrations are). They are independent properties.
Practice Quiz
Test your understanding — select the correct answer for each question.
1.What type of wave is sound?
2.What is the unit of frequency?
3.If frequency increases, what happens to pitch?
4.Calculate wave speed if f = 200 Hz and λ = 1.5 m.
5.Sound cannot travel through:
Final Study Advice
- 1.Always write the formula (v = fλ) before solving wave problems.
- 2.Draw diagrams — label crests, troughs, compressions, and rarefactions clearly.
- 3.Watch your units carefully — Hz, m, and m/s must all be consistent.
- 4.Remember that frequency affects pitch and amplitude affects loudness — never mix them up.
- 5.Practice rearranging v = fλ to solve for each variable — exams test all three forms.