Doppler Effect: Velocity of a train

In summary: So, u is the magnitude of the particle's motion, v_D is the magnitude of the particle's displacement from its initial position, and v_S is the magnitude of the particle's displacement from its final position.The student whistle is 220 Hz. The train whistle is 190 Hz when it's away from the observer. So, the train is moving at 46.4 ms-1.
  • #1
Granger
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Homework Statement


To determine the speed of a train, a student of Physics determined the frequency of the whistle in the approach to its position of observation, and measured 220 Hz. He then determined the frequency of the whistle when the train moved away, and got 190 Hz. What is the speed of train? Consider that the velocity of sound in the air is 340 ms-1

Homework Equations


[/B]
Doppler effect equation:
$$f' = f \frac{u+- v_Dt}{u+- v_St}$$

The Attempt at a Solution


What I simply did was to isolate v_D to determine it.

$$v_D=v(1-\frac{f'}{f})= 340(1+\frac{190}{200}=46.4$$

Note: I choose the minus signal in the numerator because the destiny is moving away from the source.

The answer of textbook is however:
$$v_D=v(\frac{f-f'}{f+f'})= 24.9 m/s$$

I don't get what I'm doing wrong. Can someone help me?
 
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  • #2
Maybe I'm crazy but this doppler equation doesn't feel right. Why is there a time dependence? The frequency should not be changing as a function of time. Check this.

In any case, you solved for vD. Is this the train? Which object is the source of the sound, the train or the student?
 
  • #3
Hey! You are right there is no time dependency (note that I didn't use it when doing the calculation). Sorry!

The way I interpreted the problem is that the student is the source and the train is the detector.
 
  • #5
Granger said:

Homework Statement


To determine the speed of a train, a student of Physics determined the frequency of the whistle in the approach to its position of observation, and measured 220 Hz. He then determined the frequency of the whistle when the train moved away, and got 190 Hz. What is the speed of train? Consider that the velocity of sound in the air is 340 ms-1

Homework Equations


Doppler effect equation:$$f' = f \frac{u+- v_Dt}{u+- v_St}$$

The Attempt at a Solution


What I simply did was to isolate v_D to determine it.$$v_D=v(1-\frac{f'}{f})= 340(1+\frac{190}{200}=46.4$$
Note: I choose the minus signal in the numerator because the destiny is moving away from the source.

The answer of textbook is however$$v_D=v(\frac{f-f'}{f+f'})= 24.9 m/s$$
I don't get what I'm doing wrong. Can someone help me?
Taking the time dependence out of your Doppler Effect Formula (I also assumed that you mean ±) gives:
##\displaystyle f' = f\, \frac{u\pm v_D}{u\pm v_S} ##​

Of course, the first thing to do is to give the definitions all of those quantities.
 
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Related to Doppler Effect: Velocity of a train

1. What is the Doppler Effect?

The Doppler Effect is a phenomenon that occurs when there is a perceived change in frequency of sound or light waves from a moving source towards an observer. This change in frequency is caused by the relative motion between the source and the observer.

2. How does the Doppler Effect affect sound from a moving train?

As a train moves towards an observer, the sound waves it emits will have a higher frequency due to the compression of the waves. As the train moves away from the observer, the sound waves will have a lower frequency due to the expansion of the waves. This creates the familiar "whoosh" sound as a train passes by.

3. How is the velocity of a train calculated using the Doppler Effect?

The velocity of a train can be calculated by using the formula v = fλ, where v is the velocity, f is the frequency of the sound waves, and λ is the wavelength. By measuring the change in frequency of the sound waves, the velocity of the train can be determined.

4. What factors can affect the accuracy of calculating the velocity of a train using the Doppler Effect?

The accuracy of the velocity calculation using the Doppler Effect can be affected by several factors, such as the speed of the train, the distance between the train and the observer, and any interference or obstructions in the path of the sound waves.

5. Can the Doppler Effect be applied to calculate the velocity of other moving objects?

Yes, the Doppler Effect can be applied to calculate the velocity of any moving object that emits sound or light waves. This includes objects such as cars, planes, and even stars and galaxies in space.

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