Doppler Effect Train question

So the speed of sound would be 343 m/s minus the wind speed since it's going in the opposite direction. Then you can use the formula F'=F((V+V_d)/(V-V_d)) where V is the speed of sound and V_d is the speed of the wind. So in this case, it would be F'=480((343-30)/(343+30)). This gives a frequency of approximately 439 Hz for the listener on the other train. In summary, the frequency heard on the other train is 439 Hz when one train is blowing a whistle at 480 Hz and the wind is blowing at 30.0 m/s towards the whistle and away from the listener.
  • #1
LeFerret
23
0

Homework Statement


Two trains are traveling toward each other at 30.0 m/s relative to the ground. One train is blowing a whistle at 480 Hz. (a)What frequency is heard on the other train if the wind is blowing at 30.0 m/s toward the whistle and away from the listener? (assume the speed of sound is 343m/s)

Homework Equations


F'=F((V+V_d)/(V-V_d))



The Attempt at a Solution


Well the top velocity has a + and the bottom has a minus because they're going towards each other and the wind is going away from the listener and towards the source.
So I just assumed F'=480((343+30+30)/(343-30+30)) since this is the vector sum? This is wrong however and it's actually the opposite, so I need help understanding why conceptually
 
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  • #2
You need to take each speed relative to the medium.
 

1. What is the Doppler Effect?

The Doppler Effect is a phenomenon in which the perceived frequency of a wave changes when the source of the wave is in motion relative to the observer. This change in frequency occurs because the distance between the source and observer is constantly changing, causing a shift in the wavelength of the wave.

2. How does the Doppler Effect apply to a train?

In the case of a train, the train is the source of the sound waves and the observer is the person standing on the platform. As the train approaches the observer, the sound waves are compressed, resulting in a higher frequency and a higher pitch. As the train moves away from the observer, the sound waves are stretched, resulting in a lower frequency and a lower pitch.

3. Why does the pitch of a train horn seem to change as the train passes by?

The pitch of a train horn changes because of the Doppler Effect. As the train approaches the observer, the sound waves are compressed, resulting in a higher pitch. As the train moves away from the observer, the sound waves are stretched, resulting in a lower pitch. This change in pitch is due to the relative motion between the source of the sound (the train) and the observer.

4. Does the speed of the train affect the Doppler Effect?

Yes, the speed of the train does affect the Doppler Effect. The greater the speed of the train, the greater the difference in frequency between the compressed and stretched sound waves. This means that the change in pitch will be more noticeable with a faster moving train.

5. How is the Doppler Effect used in real life?

The Doppler Effect is used in a variety of real-life applications, including radar and sonar technology, medical imaging, and astronomy. It is also used in everyday situations, such as police radar guns and weather radar. Additionally, the Doppler Effect is used in the design of musical instruments, such as wind instruments, to create different notes and pitches.

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