Doppler Effect: Train A and B Whistle Frequency Calculation

In summary, the beat frequency detected by the listener between two trains with moving whistles is 4 Hz.
  • #1
lc99
161
3

Homework Statement



Two trains A and B have a whistle that blows at a frequency fT = 392 Hz. Train A is stationary and train B is moving toward the right (away from A) at a speed of vB = 35 m/s. A listener is between the two trains and is moving toward the right with a speed of vL = 15 m/s. No wind is blowing and assume the speed of sound v = 344 m/s. What is the beat frequency fbeat detected by the listener?

Homework Equations


fL = fS [ ( V + Vl ) / (V + Vs) ]
V = 344 m/s

The Attempt at a Solution


for frequency of L by train B -
fL = 392 [ (344 - 15)/(344 +35) ] = 371.3

for train B
fL = 392 [ (344-15) / 344 ] = 374.91

375-371 = 4 = fbeat
 
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  • #2
lc99 said:

Homework Statement



Two trains A and B have a whistle that blows at a frequency fT = 392 Hz. Train A is stationary and train B is moving toward the right (away from A) at a speed of vB = 35 m/s. A listener is between the two trains and is moving toward the right with a speed of vL = 15 m/s. No wind is blowing and assume the speed of sound v = 344 m/s. What is the beat frequency fbeat detected by the listener?

Homework Equations


fL = fS [ ( V + Vl ) / (V + Vs) ]
V = 344 m/s

The Attempt at a Solution


for frequency of L by train B -
fL = 392 [ (344 - 15)/(344 +35) ] = 371.3

for train B
fL = 392 [ (344-15) / 344 ] = 374.91

375-371 = 4 = fbeat
Looks right to me.
 

FAQ: Doppler Effect: Train A and B Whistle Frequency Calculation

What is the Doppler Effect?

The Doppler Effect is the change in frequency of a sound or light wave as the source of the wave moves relative to an observer. This change in frequency is perceived as a change in pitch or color.

How does the Doppler Effect apply to trains?

In the case of trains, the Doppler Effect refers to the change in frequency of the train's whistle as it approaches or moves away from an observer. As the train approaches, the frequency of the whistle increases, and as it moves away, the frequency decreases.

What is the formula for calculating the frequency of a train whistle in the Doppler Effect?

The formula for calculating the frequency of a train whistle is f' = f(v ± vo) / (v ± vs), where f is the original frequency of the whistle, v is the speed of sound, vo is the speed of the observer, and vs is the speed of the source (train).

How does the speed of the train affect the frequency of the whistle?

The speed of the train directly affects the frequency of the whistle. As the train's speed increases, the frequency of the whistle also increases. Similarly, as the train's speed decreases, the frequency of the whistle decreases.

Can the Doppler Effect be observed with any other types of waves?

Yes, the Doppler Effect can be observed with any type of wave, including sound, light, and even water waves. It is a universal phenomenon that applies to all types of waves.

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