9702 · 7.3

Doppler effect for sound waves — practice questions

Practice and worked examples for 9702 Doppler effect for sound waves. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

A car horn emits sound with a frequency of 400 Hz. If the car is approaching a stationary observer at a speed of 30 m/s, what frequency does the observer hear? Assume the speed of sound in air is 340 m/s.

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Identify given values: Source frequency $f_s = 400$ Hz, source speed $v_s = 30$ m/s, speed of sound $v = 340$ m/s.
Choose correct sign: The car is approaching the observer, so we use the minus sign ( $-v_s$ ) in the denominator for a higher observed frequency.
Substitute values into the formula: $f_o = \frac{f_s \cdot v}{v - v_s} = \frac{400 \cdot 340}{340 - 30}$ .
Calculate: $f_o = \frac{136000}{310} \approx 438.709...$ Hz.
State answer: The observer hears a frequency of approximately 439 Hz (to 3 significant figures).

Worked example 2

A train sounds its whistle, which has a frequency of 520 Hz, as it moves away from a stationary observer at a station. The train's speed is 25 m/s. What frequency does the observer hear? Assume the speed of sound in air is 343 m/s.

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Identify given values: Source frequency $f_s = 520$ Hz, source speed $v_s = 25$ m/s, speed of sound $v = 343$ m/s.
Choose correct sign: The train is moving away from the observer, so we use the plus sign ( $+v_s$ ) in the denominator for a lower observed frequency.
Substitute values into the formula: $f_o = \frac{f_s \cdot v}{v + v_s} = \frac{520 \cdot 343}{343 + 25}$ .
Calculate: $f_o = \frac{178360}{368} \approx 484.6739...$ Hz.
State answer: The observer hears a frequency of approximately 485 Hz (to 3 significant figures).

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