Question

Two trains are traveling toward each other at 30.5m/s relative to the ground. One train is blowing a whistle at 500Hz. What frequency is heard on the other train if the wind is blowing at 30.5m/s toward the whistle and away from the listener?

Answer 1

To determine the observed frequency heard on the other train, the Doppler effect must be calculated with adjustments for the wind's influence on the speed of sound.

Step-by-step explanation:

The question involves the application of the Doppler effect in the context of two trains moving towards each other with a relative speed and considering the effect of wind on sound propagation.

Firstly, without the presence of wind, the Doppler effect can be calculated using the formula f' = f (v + v0) / (v - vs) where f' is the observed frequency, f is the source frequency, v is the speed of sound in air, v0 is the speed of the observer relative to the medium, and vs is the speed of the source relative to the medium.

However, in the presence of wind, the speed of sound is effectively changed and becomes v + vw when moving with the wind and v - vw when moving against the wind, where vw is the wind velocity.

This modified speed of sound is then utilized in the Doppler effect formula to find the observed frequency.

It should be noted that the wind assists the propagation of sound towards the listener and impedes it when going towards the source.