Question

A police car is traveling due east at a speed of 15.0 m/s relative to the earth. You are in a convertible following behind the police car. Your car is also moving due east at 15.0 m/s relative to the earth, so the speed of the police car relative to you is zero. The siren of the police car is emitting sound of frequency 500 Hz. The speed of sound in the still air is 340 m/s.
a.) What is the speed of the sound waves relative to you?
b.) What is the wavelength of the sound waves at your location?
c.) What frequency do you detect?

Answer 1

Answer:

A.) 355 m/s

B.) 0.71 m

C.) 500Hz

Explanation:

Given that a police car is traveling due east at a speed of 15.0 m/s relative to the earth. You are in a convertible following behind the police car. Your car is also moving due east at 15.0 m/s relative to the earth, so the speed of the police car relative to you is zero. The siren of the police car is emitting sound of frequency 500 Hz. The speed of sound in the still air is 340 m/s

a.) What is the speed of the sound waves relative to you?

Since the car is moving away from the observer, the relative velocity will be:

Relative velocity = 340 + 15

Relative velocity = 355 m/s

b.) What is the wavelength of the sound waves at your location?

Using the wave speed formula

V = frequency × wavelength

Make wavelength the subject of formula.

Wavelength = Velocity / frequency

Wavelength = 355/500

Wavelength = 0.71 m

c.) What frequency do you detect?

Fo = Fs ( C + V ) / ( C + v )

Fo = Fs

That is, the frequency of the observer will be equal to the frequency of the source.

Therefore, Fo = 500Hz