The Doppler Effect Video Lessons

Concept

# Problem: You are standing on a tram station platform as a tram goes by close to you. As the train approaches, you hear the whistle sound at a frequency of f1 = 94 Hz. As the train recedes, you hear the whistle sound at a frequency of f2 = 71 Hz. Take the speed of sound in air to be v = 340 m/s.(a) Find an equation for the speed of the sound source vs, in this case it is the speed of the train. Express your answer in terms of f1, f2, and v. (b) Find the numeric value, in meters per second, for the speed of the train.(c) Find an equation for the frequency of the tram whistle fs ("s" is for "source") that you would hear if the tram were not moving. Express your answer in terms of f1, f2, and v. (d) Find the numeric value, in hertz, for the frequency of the tram whistle fs that you would hear if the tram were not moving.

###### FREE Expert Solution

From the Doppler effect, we have:

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

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###### Problem Details

You are standing on a tram station platform as a tram goes by close to you. As the train approaches, you hear the whistle sound at a frequency of f1 = 94 Hz. As the train recedes, you hear the whistle sound at a frequency of f2 = 71 Hz. Take the speed of sound in air to be v = 340 m/s.

(a) Find an equation for the speed of the sound source vs, in this case it is the speed of the train. Express your answer in terms of f1, f2, and v.

(b) Find the numeric value, in meters per second, for the speed of the train.

(c) Find an equation for the frequency of the tram whistle fs ("s" is for "source") that you would hear if the tram were not moving. Express your answer in terms of f1, f2, and v.

(d) Find the numeric value, in hertz, for the frequency of the tram whistle fs that you would hear if the tram were not moving.