Two train whistles, A and B, each have a frequency of 392 Hz. A is stationary and B is moving toward the right (away from A) at a speed of 35.0 m/s. A listener is between the two whistles and is moving toward the right with a speed of 15.0 m/s.
What is the frequency from A as heard by the listener?

f_obs = 374.9 Hz

Explanation:

Given:

- Velocity of train A, V_a = 0 m/s

- Velocity of train B, V_b = 35.0 m/s

- Velocity of observer O, V_o = 15.0 m/s

Find:

What is the frequency from A as heard by the listener?

Solution:

- In this case determine the frequency of the source i.e Train A while we as listener move away from source at a velocity of 5 m/s. The variation of frequency through medium of air is related to the velocity of the sink or observer moving away or coming towards the source, as described by the Doppler's Effect in his equation:

                         f_obs = f_s * ( V_air +/- V_obs ) / ( V_air +/- V_s )

- Where,

- f_s : Frequency of the source = 392 Hz

- V_air : The velocity of sound in air = 343 m/s

- V_obs : Velocity of observer.

- V_s : Velocity of source = 0

- The frequency heard by the observer is as follows when he moves away from the source V_obs = - 15 m/s , and Velocity of source = 0. Hence using the equation:

                          f_obs = 392 * ( 343 - 15 ) / ( 343 + 0 )

                          f_obs = 374.9 Hz

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