Two train whistles have identical frequencies of 1.80 x 102 Hz. When one train is at rest in the station and the other is moving nearby, a commuter standing on the station platform hears beats with a frequency of 2.00 beats/s when the whistles operate together. What are the two possible speeds and directions that the moving train can have?

Question
Asked Dec 28, 2019
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Two train whistles have identical frequencies of 1.80 x 102 Hz. When one train is at rest in the station and the other is moving nearby, a commuter standing on the station platform hears beats with a frequency of 2.00 beats/s when the whistles operate together. What are the two possible speeds and directions that the moving train can have?

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Expert Answer

Step 1

Let f be the frequency of the whistle, fs be the frequency of the train, v be the velocity of sound, vs be the velocity of train.

Write the expression for beat frequency.

Physics homework question answer, step 1, image 1
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Step 2

Let us first take the case if the train is moving towards the station. In this case, according to the dopplers effect, the actual frequency will be more than the normal frequency.

Write the actual frequency heard by the observer.

Physics homework question answer, step 2, image 1
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Step 3

Write the expression for the frequen...

Physics homework question answer, step 3, image 1
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