Question

A police car is traveling east at 40.0 m/s along a straight road, overtaking a car ahead of it moving east at 30.0 m/s. The police car has a malfunctioning siren that is stuck at 1 000 Hz. (a) What would be the wavelength in air of the siren sound if the police car were at rest? (b) What is the wavelength in front of the police car? (c) What is it behind the police car? (d) What is the frequency heard by the driver being chased?

Answer 1

Answer:

a. The wavelength in air of the siren sound if the police car were at rest is 0.343m

b. The wavelength in front of the police car is 0.303m

c. The wavelength behind the police car is 0.383m

d. 1001.29Hz

Explanation:

Given

Speed 1 = 40m/s

Speed 2 = 30m/s

F = Frequency = 1000Hz

S = Speed of sound = 343 m/s

a.

What would be the wavelength in air of the siren sound if the police car were at rest

Stationary Wavelength λ = S/F= 343/1000= 0.343m

b.

What is the wavelength in front of the police car

Approaching Velocity = V = 40m/s

Approaching Wavelength = λ * (1 - V/S)

Where

λ = 0.343

S = 343m/s

Approaching Velocity = V = 40m/s

Approaching Wavelength = 0.343 * (1-40/343)

= 0.343 *(1 - 0.117)

= 0.343 * 0.883

= = 0.303m

c. .

What is the wavelength behind the police car

Approaching Velocity = V = 40m/s

Approaching Wavelength = λ * (1 + V/S)

Where

λ = 0.343

S = 343m/s

Approaching Velocity = V = 40m/s

Wavelength = 0.343 * (1 + 40/343)

= 0.343 *(1 + 0.117)

= 0.343 * 1.117

= 0.383m

d.

What is the frequency heard by the driver being chased?

Speed Of Approaching Police Car = 40 - 30 m/s = 10 m/s

Frequency heard, F = 1000 * (1 + 10/343) = 1029 Hz = 1.03 kHz

F = 1000 + 1+ 0.29

F = 1001.29Hz