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?

Loldi9s

Loldi9s

Open question

2022-08-21

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 & Explanation

Julius Frey

Julius Frey

Beginner2022-08-22Added 4 answers

a) To tackle this problem we will use the formula of Doppler's effect which relates the frequency of source to the frequency of listener as
f l = v + v l v + v s f s
As we are not moving relative to the source the speed of sounds relative to us is 344m/s.
b)From above we see that in our case we have that v s = v l so f l = f s which means that λ l = λ s and we obtain it's value as λ = v f = 344 500 = 0.69 m
c)Since the relative speed is zero, i.e. speeds of the listener and the source are the same we have
f l = v + v l v + v s
f l = f s
So we detect f l = 500 H z
Result:
a) v=344m/s
b) λ = 0.69 m
c) f=500Hz

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