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CAIE A-Level Physics 7.3.2 Doppler Equation for a Moving Source

Practise calculating and rearranging the Doppler equation, choosing the sign from source-observer motion and interpreting frequency, speed, units and limiting cases.

Syllabus
2028–2030
Course
Physics 9702
Level
AS

Exam points

  • calculate observed frequency using fₒ = fₛv/(v ± vₛ), choosing the sign from source–observer geometry
  • rearrange the Doppler expression to determine source frequency, source speed or wave speed
  • interpret limiting cases, units and whether motion towards or away raises or lowers frequency

7.3.2—The expression fο = f sv / (v ± vs) for the observed frequency when a source question 1

[Maximum number: 2]

A child on a sledge slides down a steep hill and then travels in a straight line up an ice-covered slope, as illustrated in Fig. 3.1.

Fig. 3.1 (not to scale)

Fig. 3.1 (not to scale)

The sledge passes point A with speed 18 ms−118 \mathrm{~ms}^{-1} at time t=0 and then comes to rest at point B. The child applies a brake to the sledge at point B. The brake does not keep the sledge stationary and it immediately slides back down the slope towards A .

The variation with time t of the velocity v of the sledge from t=0 to t=24 st=24 \mathrm{~s} is shown in Fig. 3.2.

Fig. 3.2

Fig. 3.2

The child on the sledge blows a whistle between t=4.0 st=4.0 \mathrm{~s} and t=8.0 st=8.0 \mathrm{~s}. The whistle emits sound of frequency 900 Hz . The speed of the sound in the air is 340 ms−1.A340 \mathrm{~ms}^{-1} . \mathrm{A} man standing at point A hears the sound.

Use Fig. 3.2 to

determine the initial frequency of the sound heard by the man,
initial frequency = Hz

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