Question

The siren on an ambulance is emitting a sound whose frequency is2550 Hz. The speed of sound is 343 m/s.(a) If the ambulance is stationary and you (the"observer") are sitting in a parked car, what are the wavelengthand the frequency of the sound you hear? (b)Suppose that the ambulance is moving toward you at a speed of26.3 m/s. Determine the wavelength and the frequencyof the sound you hear. (c) If the ambulance ismoving toward you at a speed of 26.3 m/s and you aremoving toward it at a speed of 12.0 m/s, find thewavelength and frequency of the sound you hear.

Answer 1

Answer:

0.13451 m

0.124196 m

0.119997901132 m

Explanation:

$v_o$ = Velocity of the observer

$v_s$ = Velocity of sound source

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

Wavelength is given by

$\lambda=\dfrac{v}{f}\\\Rightarrow \lambda=\dfrac{343}{2550}\\\Rightarrow \lambda=0.13451\ m$

The wavelength is 0.13451 m

From Doppler effect we have the formula

$f=f'\dfrac{v}{v-v_s}\\\Rightarrow f=2550\dfrac{343}{343-26.3}\\\Rightarrow f=2761.7619198\ Hz$

$\lambda=\dfrac{343}{2761.7619198}\\\Rightarrow \lambda=0.124196\ m$

The wavelength is 0.124196 m

$f=f'\dfrac{v+v_o}{v-v_s}\\\Rightarrow f=2550\dfrac{343+12}{343-26.3}\\\Rightarrow f=2858.38332807\ Hz$

$\lambda=\dfrac{343}{2858.38332807}\\\Rightarrow \lambda=0.119997901132\ m$

The wavelength is 0.119997901132 m