From the Doppler effect, we have:

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

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 f_{1} = 94 Hz. As the train recedes, you hear the whistle sound at a frequency of f_{2} = 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 v_{s}, in this case it is the speed of the train. Express your answer in terms of f_{1}, f_{2}, 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 f_{s} ("s" is for "source") that you would hear if the tram were not moving. Express your answer in terms of f_{1}, f_{2}, and v.

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

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