Question

The driver of a car traveling with speed $30m/s$ towards a hill sounds of a horn frequency $600Hz$. If the velocity of sound in air is$330m/s$, the frequency of reflected sound as heard by the driver is then
A. $500Hz$
B. $550Hz$
C. $555.5Hz$
D. $720Hz$

Answer 1

The car is the source of the sound. But, when the sound is reflected from the hill and heard by the driver, he acts as an observer. Therefore, both the source and observer are moving. The formula of the doppler effect of the sound effect has to be known to solve the problem.
Formula used:
When the source and observer both are moving, the frequency of the sound heard by the observer
${n_{^1}} = \dfrac{{V + {u_0}}}{{V - {u_s}}}n$

Complete answer:
Let, the velocity of the sound $V = 330$, velocity of the observer ${u_0} = 30$, the velocity of the source ${u_s} = 30$, sound frequency $n = 600$
Frequency of reflected sound ${n_1}$
As we know, ${n_{^1}} = \dfrac{{V + {u_0}}}{{V - {u_s}}}n$
${n_1} = \dfrac{{600 + 30}}{{600 - 30}}600Hz$
${n_1} = 720Hz$

So, the correct answer is Option D.

Note:
The Doppler effect is also known as the Doppler shift. The modifications in the frequency of any type of sound or light wave occurring by a motional source according to an observer can be defined by the doppler effect.
when the Waves are emitted by an object moving toward an observer become compressed, prompting a higher frequency since the source approaches the observer. Moreover, the waves emitted by a source moving away from an observer becomes stretched out.
If the velocity of the observer is towards the source, the velocity of the source would be positive.
If the velocity of the source is towards the observer, the velocity of the observer would be positive.
Doppler effect is observed if there is a change in frequency due to relative motion between wave sources.