Question

Carla stands on a train platform while two trains, traveling the same speed (v = 9.0 and sounding whistles of the same frequency, approach from the same direction. After one train passes Carla but before the second train passes her, she hears a beat frequency of 8.5 Hz. What is the frequency of the train whistle? f= Hz

Answer 1

To find the frequency of the train whistle, subtract the beat frequency from the known frequency of one of the train whistles.

Step-by-step explanation:

When two moving objects are emitting sound waves, there is a change in the frequency of the sound waves detected by a stationary observer due to the Doppler effect.

In this case, Carla is stationary on the train platform while the two trains are approaching from the same direction at the same speed.

The beat frequency that Carla hears is the difference between the frequencies of the two train whistles. So, the frequency of the train whistle can be found by subtracting the beat frequency from the known frequency of one of the train whistles.

Answer 2

To find the frequency of the train whistle, we need to understand the Doppler effect and use the beat frequency heard by Carla. Without the frequency heard after the first train passes (receding frequency), we cannot calculate the original frequency of the train whistle given only the beat frequency.

Step-by-step explanation:

The question involves understanding the concept of the Doppler effect, which is a change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. In this scenario, Carla hears a beat frequency of 8.5 Hz when one train has passed and the other is approaching. The beat frequency is the difference between the frequency of the sound wave when the source is approaching and when the source is receding.

To solve for the frequency of the train whistle, we can use the formula:

f = (f_{beat} + f_{receding}) / 2,

where f is the original frequency of the train whistle, f_{beat} is the beat frequency, and f_{receding} is the frequency heard after the train has passed.

To find f_{receding}, we would use the Doppler effect formula for a receding source, but since the actual frequency f is what we are looking for, and we are not given f_{receding}, we cannot calculate it without additional information.