Two train whistles have identical frequencies of 1.80 ∗ 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 per second when the whistles operate together. what are the possible speeds and directions that the moving train can have? [3.85 m/s or 3.77 m/s]

The source speed toward the station and away from the station are 3.79 m/s and 3.87 m/s.

Explanation:

Given that,

Frequency of the whistles f = 1.80\times10^{2}\ Hz[/tex]

Beat frequency = 2.00 b/s

We need to calculate the frequency

Using formula of beat frequency

Put the value into the formula

When the train moving towards station, then the frequency heard is more than the actual

We need to calculate the source speed

Using Doppler effect

Therefore, the source speed is

Put the value into the formula

When the train moving away from the station, then the frequency heard is

Again from beat frequency,

Put the value into the formula

We need to calculate the source speed

Using Doppler effect

Therefore, the source speed is

Put the value into the formula

Hence, The source speed toward the station and away from the station are 3.79 m/s and 3.87 m/s.

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