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 992 Hz.
What is the wavelength behind the police car in meters?
Lr = Ls * (1 + (vr / c))
To find the wavelength behind the police car, we need to know the speed of sound in air. The speed of sound in air is approximately 343 m/s at standard temperature and pressure.
First, we need to find the speed of the police car relative to the stationary air. Since both the police car and the car ahead are moving east, we can subtract their velocities to find the police car's velocity relative to the stationary air.
Relative velocity of the police car = Velocity of the police car - Velocity of the car ahead
Relative velocity of the police car = 40.0 m/s - 30.0 m/s
Relative velocity of the police car = 10.0 m/s
Now, to find the wavelength, we can use the formula:
Wavelength = Speed of sound / Frequency
Using the given frequency of the malfunctioning siren (992 Hz) and the speed of sound in air (343 m/s):
Wavelength = 343 m/s / 992 Hz
Calculating the wavelength:
Wavelength = 0.345 m
Therefore, the wavelength behind the police car is approximately 0.345 meters.