Home / CIE AS & A Level Physics : 7.3 Doppler effect for sound waves – Exam style question – Paper 1
An aircraft flies at a velocity \(v_s\) directly away from a stationary observer.
The aircraft emits a sound of constant frequency.
The speed of sound in air is \(v\).
The frequency of the sound heard by the observer on the ground is \(500\,\mathrm{Hz}\).
The speed of the aircraft is increased so that it flies away from the observer at a greater velocity.
The observer now hears a sound of frequency \(250\,\mathrm{Hz}\).
Which expression gives the new velocity of the aircraft?
Correct Answer: \( \boxed{\mathrm{C}} \)
For a source moving away, \(f’ = f\dfrac{v}{v+v_s}\).
Halving the observed frequency requires doubling the denominator:
\(v+v_{\text{new}}=2(v+v_s)\).
Hence, \(v_{\text{new}}=v+2v_s\).
Therefore, the correct answer is (C).
A dolphin is swimming at a speed of \( 16.0\,\mathrm{m\,s^{-1}} \) directly towards a stationary underwater microphone.
The dolphin emits a sound of frequency \( 122\,\mathrm{kHz} \). The speed of sound in water is \( 1480\,\mathrm{m\,s^{-1}} \).
What is the frequency of sound detected by the microphone?
Correct Answer: \( \boxed{\mathrm{D}} \)
For a source moving towards a stationary observer, the Doppler equation is
\( f’ = f\left(\dfrac{v}{v-v_s}\right) \).
Substituting \( f=122\,\mathrm{kHz} \), \( v=1480\,\mathrm{m\,s^{-1}} \), and \( v_s=16.0\,\mathrm{m\,s^{-1}} \),
\( f’ = 122\left(\dfrac{1480}{1480-16}\right)\approx122\left(\dfrac{1480}{1464}\right)\approx123.3\,\mathrm{kHz} \).
To three significant figures, the detected frequency is \( 123\,\mathrm{kHz} \).
Therefore, the correct answer is (D).
The diagram shows a car travelling at a constant speed in a straight line between person P and person Q from point \(X\) to point \(Y\).
The car sounds its horn continuously as it travels. The horn emits sound of constant frequency.
Which statements about what person P and person Q hear during the motion of the car are correct?
1. Person P hears a sound of increasing frequency.
2. Person Q hears a sound of decreasing frequency.
3. Person Q always hears a sound of higher frequency than person P.
Correct Answer: \( \boxed{\mathrm{C}} \)
Person P is behind the moving car and hears a lower frequency because the source is moving away, while person Q is in front of the car and hears a higher frequency because the source is approaching.
The frequency heard by each observer remains constant while the car moves at constant speed, so statements 1 and 2 are incorrect.
Person Q always hears a higher frequency than person P, so statement 3 is correct.
Therefore, the correct answer is (C).