Question

a train whistle is heard at 270 hz as the train approaches town. the train cuts its speed in half as it nears the station, and the sound of the whistle is then 260 hz. what is the speed of the train before slowing down?

Answer 1

The speed of the train before slowing down can be calculated using the Doppler effect equation. The given frequencies of the train whistle and the speed of sound are used to find the relative velocity of the observer and the source.

Step-by-step explanation:

The frequency of a sound wave is affected by the relative motion between the source of the sound and the observer. This is known as the Doppler effect. In this case, as the train approaches the town, its speed is halved, resulting in a change in frequency of the train whistle.

To find the speed of the train before slowing down:

1. Use the equation fobs = fs * (v + Vr)/(v + Vs), where fobs is the observed frequency, fs is the source frequency, v is the speed of sound, Vr is the relative velocity of the observer and the source moving away from each other, and Vs is the relative velocity of the observer and the source moving towards each other.
2. Substitute the given values: fobs = 260 Hz, fs = 270 Hz, v = speed of sound, and Vr = Vs/2.
3. Solve the equation for Vs, which represents the speed of the train before slowing down.

The calculated value of Vs will give you the speed of the train before it slows down.