Question

A car giving horn is moving towards a crossing as shown in figure. At the instant when the observer O hears the same frequency as the frequency as the horn, the car will be
A. Between A and X
B. Between X and B
C. At X
D. Before A

Answer 1

Hint:In the above question, we have to note the change in the sound of car horn moving with a constant velocity. The phenomena which observe the change in the wave frequency is known as doppler effect. Doppler effect is produced by moving source (car) in which there is upward shift when source is approaching towards the observer and downward shift when source is receding from the observer.

Complete answer:
Doppler effect is defined as the change in the frequency of wave during relative motion between a source and its observer.
${f_o} = \dfrac{{v + {v_o}}}{{v + {v_s}}}{f_s}$
Where ${f_o}$ is the observer frequency, $v$ is the speed of sound waves, ${v_o}$ is observer velocity, ${v_s}$ is the source velocity and ${f_s}$ is the frequency of source.

In our above question, we want to know the position of the car where it will observe the same frequency. To solve this let us calculate frequency at every point given in question
Between A and X: in this path the car is observing the point O, hence by doppler shift will observe upward shift.
Between X and B: in this path the car is receding the point O and will observe downward shift.
At X: It will observe the same frequency as at O which is the required answer.
The correct option is C.

Note:If the source is still and the observer is moving will give the same result as when the source is moving and the observer is still. Just keep in mind that when the source is approaching the observer there will be an upward shift and when the source is receding the observer there will be a downward shift.