Question

step by step pls

In an attempt to get the last parking spot at West Edmonton Mall, a car speeds towards the outside wall of the mall with its horn sounding a frequency of 160.0 Hz. The sound waves reflected off the wall cause the driver to hear 8.0 beats per second. Find the speed of the car. There is no wind blowing and the speed of sound in air is 343 m/s.

Answer 1

The car travelling at speed v sounds its horn. The sound waves approaching the wall are doppler shifted to a higher frequency f1 by the doppler formula:

f1 = (1 + v/c) f0 where c = speed of sound in air and f0 = frequency of horn at rest.

The waves are reflected but now the car is moving toward what appears to be the source of a sound of frequency f1 so there is again a upshift in frequency to f2

f2 = (1 +v/c) f1

f2 = (1 + v/c)^2 f0

Now since the driver hear 8 beats per second, it means the driver hears a frequency of 160 + 8 = 168 Hz

=> 168 = (1+v/c)^2*160

=> 168/160 = (1+v/c)^2

1.05 = (1+v/c)^2

1 + v/c = 1.0246

v/c = 0.0246

v = 0.0246*343 = 8.43 m/s