A police car moving away from a stationary observer with siren on. The frequency of police siren is 500 Hz. The speed of sound in air is 343 m/s.

A) What is the wavelength of people siren?

B) A stationary observer measures the frequency of siren to be 450 Hz. Find the speed of police car.

A)

The wavelength of people siren λ = 0.686 m

B)

The speed of police car vs = 38.11 m/s

Step-by-step explanation

Given the following data

The frequency of police siren = 500 Hz

The speed of sound in air = 343 m/s

A) What is the wavelength of people siren?

Solution

Formula

λ = v/f

Where λ is the wavelength of people siren

v is the speed of sound in air = 343 m/s

f is the frequency of police siren = 500 Hz

λ = v/f = (343 m/s)/(500 Hz )

λ = 0.686 m

The wavelength of people siren λ = 0.686 m

B) A stationary observer measures the frequency of siren to be 450 Hz. Find the speed of police car.

Solution

Formula

f = f_o(v/(v-vs))

Where f is the frequency of stationary observer = 450 Hz

f_o is the frequency of police siren = 500 Hz

v is the speed of sound in air = 343 m/s

vs is the speed of the source = the speed of police car

450 Hz = 500 Hz(343 m/s/(343 m/s - vs))

450 Hz/500 Hz = 500 Hz(343 m/s/(343 m/s - vs))

(343 m/s - vs)0.9 = 343 m/s

308.7 - 0.9 vs = 343 m/s

0.9 vs = 308.7 - 343 m/s

vs = -34.3/0.9

vs = -38.11 m/s ( ignore the negative sign)

vs = 38.11 m/s

The speed of police car vs = 38.11 m/s