The Doppler Effect and Shock Waves · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Why the siren changes pitch as it passes

Science · Waves, Light & Sound · ages 18-20
Name ______________________   Date ____________

  1. In still air, compare a moving source with a stationary listener, then a stationary source with a moving listener. Which describes the mechanisms?

    • Both change sound speed in the air, without changing how often waves arrive.
    • Source motion changes spacing; listener motion changes encounter rate.
    • Both change the emitted frequency, without changing wave spacing in the air.

  2. A steady siren approaches a stationary listener in still air at less than sound speed. Why does the listener hear a higher pitch?

    • Motion packs compressions closer together ahead
    • Motion makes sound travel faster through the air
    • Motion makes the siren emit more cycles each second

  3. A jet produces a sonic boom only at the instant it first exceeds sound speed.

    Circle one:   True   False

  4. A siren emits 600 Hz and moves directly away from a stationary listener at 60 m/s in still air. Sound speed is 300 m/s. What frequency is heard?

    • 500 Hz
    • 600 Hz
    • 750 Hz

  5. A stationary horn emits 600 Hz in still air where sound speed is 300 m/s. A listener moves directly toward it at 30 m/s. What frequency is heard?

    • 540 Hz
    • 600 Hz
    • 660 Hz

  6. In the ideal Mach-cone model, a source moves at twice the sound speed. What is sin θ, where θ is the cone half angle?

    Answer: ______________

  7. In still air, f_s = 100 Hz and v = 300 m/s. Compare approach at 240 m/s along the joining line: a moving source with a stationary listener, then a moving listener with a stationary source. Which heard frequencies are correct?

    • Source: 180 Hz; listener: 500 Hz
    • Source: 500 Hz; listener: 500 Hz
    • Source: 500 Hz; listener: 180 Hz

  8. An ideal Mach cone has sin θ = 0.25. How fast is its source compared with sound speed v?

    • One quarter of sound speed
    • Four times sound speed
    • Three quarters of sound speed
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Why the siren changes pitch as it passes W1-mt_UVfD_coqh6-s1

  1. Source motion changes spacing; listener motion changes encounter rate. · Moving the emission point changes compression spacing. Moving the listener through an existing wave changes the rate of meeting compressions.
  2. Motion packs compressions closer together ahead · The emitted frequency stays fixed. Source motion shortens compression spacing ahead, so more compressions reach the listener each second.
  3. False · A jet can keep producing shocks during supersonic flight. A listener hears a boom when a shock reaches them.
  4. 500 Hz · For a receding source, f_o = 600 × 300 ÷ (300 + 60) = 500 Hz.
  5. 660 Hz · For an approaching listener, f_o = 600 × (300 + 30) ÷ 300 = 660 Hz.
  6. 0.5 · sin θ = v ÷ u_s. With u_s = 2v, this is 1 ÷ 2 = 0.5.
  7. Source: 500 Hz; listener: 180 Hz · Source motion gives 100 × 300 ÷ 60 = 500 Hz. Listener motion gives 100 × 540 ÷ 300 = 180 Hz. Equal approach speeds give different shifts.
  8. Four times sound speed · Rearrange sin θ = v ÷ u_s to u_s = v ÷ sin θ. Dividing v by 0.25 gives 4v.
Worksheet · LightMySky