Physics 9702 · AS & A Level · Doppler effect for sound waves
Doppler effect for sound waves — practice question
A train moves at constant speed along a straight horizontal track towards an observer who is standing next to the track, as shown in Fig. 6.1. As it nears the observer, the train’s horn is sounded continuously. The horn produces a sound with constant frequency $251\,\text{Hz}$. The frequency heard by the observer is $291\,\text{Hz}$. The speed of sound in air is $340\,\text{m s}^{-1}$.
(a)[2]
Calculate the speed at which the train is moving.
(b)
The train approaches the observer and then passes by. The intensity $I$ of the sound heard by the observer depends on the distance $d$ of the horn from the observer. When the horn is at a distance $x_0$ from the observer, the intensity $I$ of the sound heard is $I_0$ and the amplitude $A$ of the sound wave at the observer is $A_0$. Fig. 6.2 shows how $I/I_0$ changes with $d/x_0$ as the train moves away from the observer.
(b(i))[1]
State the relationship linking amplitude $A$ and intensity $I$ for a progressive wave.
(b(ii))[2]
On Fig. 6.3, sketch how $A/A_0$ varies with $d/x_0$.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “291 = 251 \times \frac{340}{340 - v_s}” …