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A train is traveling at 30.0 m/s relative to the ground in still air. The frequency of the note emitted by the train whistle is 262 Hz. The speed of sound in air should be taken as 344 m/s. Part A

What frequency fapproach is heard by a passenger on a train moving at a speed of 18.0 m/s relative to the ground in a direction opposite to the first train and approaching it?

Express your answer in hertz.

Part B

What frequency frecede is heard by a passenger on a train moving at a speed of 18.0 m/s relative to the ground in a direction opposite to the first train and receding from it?

Express your answer in hertz.

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Answer:

302.05 Hz

228.37433 Hz

Explanation:

v = Speed of sound in air = 344 m/s

[tex]v_r[/tex] = Speed of train relative to the ground in a direction opposite to the first train and approaching it = 18 m/s

[tex]v_r[/tex] = Speed of train relative to the ground in still air = 30 m/s

The frequency of approach is given by

[tex]f'=f\frac{v+v_r}{v-v_s}\\\Rightarrow f'=262\frac{344+18}{344-30}\\\Rightarrow f'=302.05\ Hz[/tex]

The frequency of approach is 302.05 Hz

The frequency of recede is given by

[tex]f'=f\frac{v-v_r}{v+v_s}\\\Rightarrow f'=262\frac{344-18}{344+30}\\\Rightarrow f'=228.37433\ Hz[/tex]

The frequency of recede is 228.37433 Hz

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