Question

A commuter train passes a passenger platform at a constant speed of 37.3 m/s. The train horn is sounded at its characteristic frequency of 336 Hz. (a) What overall change in frequency is detected by a person on the platform as the train moves from approaching to receding?

Answer 1

When a train moves towards a stationary person, the sound waves are compressed, resulting in an increase in frequency. Conversely, when the train moves away from the person, the sound waves are stretched, resulting in a decrease in frequency. The overall change in frequency detected by a person on the platform as the train moves from approaching to receding is 37.687 Hz.

Step-by-step explanation:

When a train moves towards a stationary person, the sound waves are compressed, resulting in an increase in frequency. This is known as the Doppler effect. Conversely, when the train moves away from the person, the sound waves are stretched, resulting in a decrease in frequency.

To calculate the overall change in frequency detected by a person on the platform, we can use the equation:

Δf = (vt / vs) × f

Where:

• Δf is the change in frequency
• vt is the speed of the train
• vs is the speed of sound
• f is the characteristic frequency of the train horn

Plugging in the given values:

Δf = (37.3 m/s / 335 m/s) × 336 Hz

Δf = 37.687 Hz

Therefore, the overall change in frequency detected by a person on the platform as the train moves from approaching to receding is 37.687 Hz.