Diffraction & the Doppler Effect
Sound bends round corners, and an approaching siren sounds higher.
Lesson at a glanceShow the key points
- Diffraction: waves bend around obstacles and spread from openings, strongly when their size is comparable to or smaller than λ. Audible sound has λ from about 1.7 cm to 17 m, so it diffracts readily.
- Source approaching a still observer: ν′ = vν/(v − u) (16.23); receding: vν/(v + u) (16.24).
- Observer approaching a still source: ν′ = (v + u)ν/v (16.25); receding: (v − u)ν/v (16.26).
- General: ν′ = (v + u₀)ν/(v − uₛ) (16.27), speeds relative to the medium, positive toward the other; use components along the line joining them.
- A moving source changes the wavelength ahead to λ′ = (v − u)λ/v (16.28).
You can hear someone talking in the next room through an open door, even though you can’t see them. And an ambulance’s siren drops in pitch the moment it passes you. Both are everyday wave effects.
Diffraction
When a wave meets an obstacle or passes through an opening, it spreads into the region that a straight-line path would leave in shadow. This bending is diffraction. It is strong when the obstacle or opening is about the size of the wavelength or smaller, and weak when it is much larger.
Audible sound has wavelengths from about 1.7 cm (20 kHz) to 17 m (20 Hz), similar to doors, windows, furniture and people. So sound diffracts easily around everyday objects, while light, with a wavelength under a micrometre, does not. That is why you hear around corners but can’t see around them. Low notes bend around more than high ones: from the next room, music sounds bass-heavy.
The Doppler effect
When a source of sound and a listener move toward each other, the listener hears a higher frequency than the source emits; when they move apart, a lower one. This is the Doppler effect. All speeds below are measured relative to the air (the medium). Let v be the speed of sound and ν the frequency emitted.
Source moving, observer at rest
The source sends out a compression every period T = 1/ν. In that time the previous compression has travelled vT, but the source has moved uT after it. So the compressions ahead of it are only (v − u)T apart. They reach the observer at speed v, so the observer hears them at intervals of (v − u)T/v:
Here the wavelength itself changes. Ahead of the source:
Observer moving, source at rest
Now the wavelength is normal, λ = v/ν, but the observer runs into the compressions faster. Moving toward the source at u₀, the compressions pass at relative speed v + u₀:
Both moving
An ambulance siren emits 700 Hz and drives at 25 m/s past a listener standing on the pavement. Speed of sound 340 m/s. What does the listener hear before and after it passes?
Now the 700 Hz siren is parked, and a cyclist rides toward it at 20 m/s. What frequency does the cyclist hear?
- 1Diffraction is strong when obstacles or openings are about the wavelength; sound (λ ≈ 1.7 cm–17 m) bends around everyday objects.
- 2Moving source: ν′ = vν/(v ∓ uₛ); the wavelength ahead shrinks to (v − uₛ)λ/v.
- 3Moving observer: ν′ = (v ± u₀)ν/v; the wavelength is unchanged.
- 4General: ν′ = (v + u₀)ν/(v − uₛ), speeds relative to the medium, positive toward each other, components along the joining line.
Check yourself
Keep exploring
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