Question

An ambulance is traveling north at 60.3 m/s, approaching a car that is also traveling north at 33.4 m/s. The ambulance driver hears his siren at a frequency of 696 Hz. Ambulance 60.3 m/s 33.4 m/s Car What is the wavelength at any position in front of the ambulance for the sound from the ambulance’s siren? The velocity of sound in air is 343 m/s. Answer in units of m.

Answer 1

Answer:

0.44999 m

Explanation:

f = Actual wavelength = 696 Hz

v = Speed of sound in air = 343 m/s

$v_o$ = Velocity of observer = 33.4 m/s

$v_s$ = Velocity of source = 60.3 m/s

From Doppler's effect we have

$f_o=f\left(\dfrac{v-v_o}{v-v_s}\right)\\\Rightarrow f_o=696\left(\dfrac{343-33.4}{343-60.3}\right)\\\Rightarrow f_o=762.22709\ Hz$

Wavelength is given by

$\lambda=\dfrac{v}{f}\\\Rightarrow \lambda=\dfrac{343}{762.22709}\\\Rightarrow \lambda=0.44999\ m$

The wavelength at any position in front of the ambulance for the sound from the ambulance’s siren is 0.44999 m.