Sound Waves & the Doppler Effect

You’ll be able to

Describe sound as a longitudinal pressure wave and relate its properties to what we hear
Apply v = fλ to sound in air
Explain the Doppler effect for a source moving relative to an observer

Sound is a longitudinal pressure wave

Sound is a longitudinal wave: the air molecules oscillate back and forth along the direction the wave travels, creating alternating compressions (high pressure) and rarefactions (low pressure). Sound needs a medium — it cannot travel through a vacuum. What we hear maps onto wave properties: frequency sets the pitch (high frequency = high pitch), and amplitude sets the loudness. In room-temperature air, sound travels at about 343 m·s⁻¹, far slower than light, which is why you see lightning before you hear thunder.

Wave relationship for sound

v = f · λ (v ≈ 343 m·s⁻¹ in air at room temperature)

The same v = fλ governs sound. A higher-pitched note (larger f) has a shorter wavelength in the same air.

The Doppler effect

When a sound source moves relative to a listener, the observed frequency shifts — the Doppler effect. As a source approaches, each successive wavefront is emitted a little closer, bunching the waves up: the wavelength shortens and the observed frequency rises (higher pitch). As the source recedes, the waves stretch out and the pitch drops. You hear this every time a siren passes: high as it comes, suddenly lower as it goes. The source’s actual frequency never changes — only what the listener receives.

Worked example

A sound wave travels through air at 340 m·s⁻¹ with a frequency of 170 Hz. What is its wavelength?

1.Rearrange v = fλ to solve for wavelength: λ = v/f.
2.Substitute: λ = 340 / 170.
3.Divide: 340 / 170 = 2.0.

Answer: λ = 2.0 m.

Checkpoint

A sound wave travels at 340 m·s⁻¹ with a frequency of 170 Hz. What is its wavelength?

Watch out

In the Doppler effect, the source’s emitted frequency is unchanged — it is the observed frequency that shifts because the relative motion compresses or stretches the wavefronts. Do not say the siren “changes its frequency”; the listener simply receives a different one.

Checkpoint

A siren moves directly toward a stationary observer. Compared with the frequency the siren emits, the observer hears a frequency that is:

On the exam

Doppler shorthand: approaching → higher pitch (compressed waves), receding → lower pitch (stretched waves). The dramatic drop you hear as a vehicle passes is the switch from approaching to receding at the instant it goes by.

Answer the 2 checkpoints as you read.