The Doppler Effect Video Lessons

Concept

# Problem: A student knows that an ambulance siren has a frequency of fs =  396 Hz. He measures, when the ambulance is approaching him, the frequency fo = 417 Hz. Assume the speed of sound is 343 m/s in this problem. Part a) Input an expression for the ambulance's speed v in terms of the frequencies and the speed of sound v. Part b) what is this speed, in meters per secondPart c) If ambulance is moving away with the same speed as in part (b) what is the wavelength measured by the student in meters ?

###### FREE Expert Solution

Part a)

From the Doppler effect:

$\overline{){{\mathbf{f}}}_{{\mathbf{0}}}{\mathbf{=}}\mathbf{\left(}\frac{\mathbf{v}}{\mathbf{v}\mathbf{-}{\mathbf{v}}_{\mathbf{s}}}\mathbf{\right)}{{\mathbf{f}}}_{{\mathbf{s}}}}$

Solving for vs:

$\begin{array}{rcl}\mathbf{v}\mathbf{-}{\mathbf{v}}_{\mathbf{s}}& \mathbf{=}& \frac{{\mathbf{f}}_{\mathbf{s}}}{{\mathbf{f}}_{\mathbf{0}}}\mathbf{v}\\ {\mathbf{v}}_{\mathbf{s}}& \mathbf{=}& \mathbf{v}\mathbf{-}\frac{{\mathbf{f}}_{\mathbf{s}}}{{\mathbf{f}}_{\mathbf{0}}}\mathbf{v}\\ & \mathbf{=}& \mathbf{v}\mathbf{\left(}\mathbf{1}\mathbf{-}\frac{{\mathbf{f}}_{\mathbf{s}}}{{\mathbf{f}}_{\mathbf{0}}}\mathbf{\right)}\end{array}$

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###### Problem Details

A student knows that an ambulance siren has a frequency of fs =  396 Hz. He measures, when the ambulance is approaching him, the frequency fo = 417 Hz. Assume the speed of sound is 343 m/s in this problem.

Part a) Input an expression for the ambulance's speed v in terms of the frequencies and the speed of sound v.

Part b) what is this speed, in meters per second

Part c) If ambulance is moving away with the same speed as in part (b) what is the wavelength measured by the student in meters ?