Question

as you stand by a railroad track, a train approaches with its whistle blowing. after the train has passed you, you hear that the whistle frequency is 18.0% lower than its frequency while the train was approaching. how fast is the train moving? express your answer in km/hr. (note that the speed of sound that day is 333.3 m/s.)

Answer 1

The train is moving at a speed of approximately 215.98 km/hr.

Step-by-step explanation:

The phenomenon described in the question is known as the Doppler effect.

The Doppler effect explains the change in frequency of a wave, such as sound or light, due to the relative motion between the source of the wave and the observer.

In this case, as the train moves away from the observer, the frequency of the whistle appears lower. The change in frequency can be calculated using the formula:

Δf = (v/vs) * f

Where Δf is the change in frequency, v is the speed of sound, vs is the speed of the source (train), and f is the original frequency of the whistle.

Using the given values of Δf = -18% * f and v = 333.3 m/s, we can solve for vs, the speed of the train.

vs = (Δf/f) * v

vs = (-18% * f/f) * 333.3 m/s

vs = -0.18 * 333.3 m/s

vs = -59.994 m/s

Since the speed of the train cannot be negative, we take the magnitude of the speed:

Speed of train = |vs| = 59.994 m/s

To convert the speed to km/hr, multiply by 3.6:

Speed of train = 59.994 m/s * 3.6 = 215.9784 km/hr

Therefore, the speed of the train is approximately 215.98 km/hr.