Question

You are standing on a sidewalk. There is a car in the distance. The horn on the car sounds. You hear it at a pitch that corresponds to a sound frequency lower than the frequency emitted by the horn. What can you conclude?A) Either A or C must be true.B) The car is moving on a line directly away from your present location.C) The wind has a component of its velocity in a direction away from you.D) The car has a component of its velocity in a direction away from you.E) The wind has a component of its velocity in a direction toward you.

Answer 1

Answer: The answer: The car is moving away from you.

Both A and C are true as Car can be moving in line away from you or has component of velocity in opposite direction.

Explanation:The decrease in the frequency of the sound is the result of Doppler's effect. A/c to Doppler's effect the frequency of received sound of source is changed if it is moving relative to the receiver, i.e. the distance between them is changing due to motion.

The general formula of Doppler's Effect is attached as the picture.

In this formula v_D is the velocity of Detector i.e the receiver relative to wind. While v_s is the velocity of source relative to wind and v is the velocity of sound.

The Doppler's effect is not effected by the velocity of wind as the wind itself could not change the distance between the two objects i.e. you and the car. Wind velocity can change the speed of sound and its wavelength but the change does not effect the frequency.

Hence if we assume the car to be moving with velocity v_c and you are stationary

$f'=f_s*\frac{v}{v-v_c}$

hence the frequency is reduced.