Question 503: Waves

Question

A stationary source emits sound of frequency $${f_0} = 492\,Hz.$$ The sound is reflected by a large car approaching the source with a speed of $$2\,m{s^{ - 1.}}$$ The reflected signal is received by the source and superposed with the original.
What will be the beat frequency of the resulting signal in $$Hz$$? (Given that the speed of sound in air is $$330\,m{s^{ - 1}}$$ and the car reflects the sound at the frequency it has received).

Accepted Answer

It is given that the source emits sound of frequency f
0
= 492 Hz. The car is approaching the source and the speed of car is v = 2 m/s.
Also, the speed of sound in air, v
s
= 330 m/s.
The frequency of sound received by car is given as
$${f_1} = \left( {{{{V_s} + V} \over {{V_s}}}} \right){f_0} = \left( {{{330 + 2} \over {330}}} \right)492$$
Here, f
1
= 494.98 Hz, which is the frequency reflected by the car towards the source.
Therefore, now, the car acts as the source. The frequency of sound received by the source is
$${f_2} = \left( {{{{V_s}} \over {{V_s} - v}}} \right){f_1} = \left( {{{330} \over {330 - 2}}} \right)494.98$$
Here, f
2
= 498 Hz. Therefore, the beat frequency of the resulting signal is
$$\left| {{f_0} - {f_2}} \right| = \left| {492 - 498} \right| = 6$$ Hz

Waves

Integer / Numeric Answer Type