Waves & Sound
Understand transverse and longitudinal waves, use the wave equation, and explore the Doppler effect that changes the pitch of a passing ambulance siren.
Types of Waves
A wave is a disturbance that transfers energy through a medium (or through space) without transferring matter. Waves are classified by the direction of the particle vibration relative to the direction of wave travel.
Transverse Waves
Particles vibrate perpendicular (at right angles) to the direction of wave travel.
Examples: Light waves, water waves, waves on a string, seismic S-waves
Longitudinal Waves
Particles vibrate parallel to the direction of wave travel, forming compressions and rarefactions.
Examples: Sound waves, seismic P-waves, a slinky pushed lengthwise
Wave Properties & the Wave Equation
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). 1 Hz = 1 wave per second.
Amplitude (A)
The maximum displacement of a particle from its rest position. Determines the energy (loudness or brightness) of the wave.
Wave speed (v)
How fast the wave travels through a medium. Measured in m/s. Sound travels at ~343 m/s in air at 20°C.
The Wave Equation
v = f λ
v = wave speed (m/s)
f = frequency (Hz)
λ = wavelength (m)
Sound & the Doppler Effect
Sound is a longitudinal mechanical wave — it requires a medium (solid, liquid or gas) to travel through. It cannot travel through a vacuum. In air at 20°C, sound travels at approximately 343 m/s.
The Doppler Effect
The Doppler effect is the observed change in frequency (pitch) of a wave as the source and observer move relative to each other.
- Source approaching: Waves are compressed in front of the source → wavelength decreases → frequency increases → higher pitch
- Source moving away: Waves are stretched behind the source → wavelength increases → frequency decreases → lower pitch
Australian example: An ambulance siren sounds higher in pitch as it approaches and lower as it passes and drives away. Police speed radar and weather radar also use the Doppler effect.
Pitch & Frequency
Higher frequency sound = higher pitch. Humans can hear 20 Hz–20 000 Hz. Ultrasound is above 20 000 Hz (used in medical imaging).
Loudness & Amplitude
Greater amplitude = louder sound. Loudness is measured in decibels (dB). Prolonged exposure to sounds above 85 dB can damage hearing.
Speed in Different Media
Sound travels faster in solids (5 000 m/s in steel) than liquids (1 500 m/s in water) or gases (343 m/s in air).
Key Vocabulary
| Term | Definition |
|---|---|
| Frequency | The number of complete wave cycles passing a fixed point per second; measured in hertz (Hz). |
| Wavelength | The distance between two consecutive points in phase on a wave, such as crest to crest. |
| Amplitude | The maximum displacement of a particle from its rest (equilibrium) position. |
| Doppler effect | The apparent change in the frequency of a wave due to relative motion between the source and the observer. |
Worked Examples
Finding wave speed using the wave equation.
Given: A sound wave has a frequency of 440 Hz and a wavelength of 0.78 m.
Step 1: v = f × λ
Step 2: v = 440 × 0.78
Answer: v = 343.2 m/s (consistent with the speed of sound in air at room temperature).
Calculating wavelength from speed and frequency.
Given: A radio wave travels at 3 × 108 m/s with a frequency of 100 MHz (1 × 108 Hz).
Step 1: Rearrange: λ = v ÷ f
Step 2: λ = 3 × 108 ÷ 1 × 108
Answer: λ = 3 m
Explaining a Doppler effect observation.
Scenario: A train blows its horn (f = 500 Hz) as it approaches the station at high speed. A passenger on the platform hears a frequency higher than 500 Hz.
Explanation: As the train approaches, sound waves emitted forward are compressed (shorter wavelength). Because v = fλ and v is constant in the medium, shorter λ means higher f.
Answer: The platform observer hears a higher pitch than 500 Hz as the train approaches. Once the train passes and moves away, the waves behind it are stretched, reducing f, so the pitch drops below 500 Hz.
Knowledge Check
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Key Concepts Summary
- •Transverse waves: particle vibration is perpendicular to wave travel (e.g., light, water waves).
- •Longitudinal waves: particle vibration is parallel to wave travel; form compressions and rarefactions (e.g., sound).
- •The wave equation: v = fλ; rearrange to find any of the three quantities.
- •Sound travels at ~343 m/s in air; faster in liquids and solids; cannot travel through a vacuum.
- •The Doppler effect: a source approaching causes higher observed frequency; moving away causes lower frequency.