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