# A question about the Doppler efffect

• taculator
In summary, the conversation discusses a problem involving a commuter train passing a passenger platform at a constant speed and the detection of its horn's characteristic frequency by a person on the platform. The solution involves using equations for frequency and wavelength, and the conversation also discusses the confusion over the source and detector frequencies and the impact of the approximation used in the solution. The final answer for the change in frequency is approximately 75 Hz.
taculator

## Homework Statement

A commuter train passes a passenger platform at a constant speed of 40 m/s. The train horn is sounded at its characteristic frequency of 320 hz. A) What change in frequency is detected by a person on the platform as the train passes? B) What wavelength is detected by a person on the platform as the train approaches?

## Homework Equations

Frequency of detector = (Velocity of Sound+/- Velocity of Detector)/(Velocity of Sound +/- Velocity of Source) times Frequency of Source

## The Attempt at a Solution

since the source (train) is moving towards the detector( person on platform) intially i did
Fd= (Vsound)/(Vsound+40) times Fs

where f is frequency
fd is 320 hz
and vsound is 343 m/s

I plugged in and i got that the frequency of the source was 282.7 hz, and then I plugged that into

Fd= (Vsound)/(Vsound-40) times Fs

because that would be the frequency of the detector as the train passes away.
After doing this I found that the change in frequency to be about 84 hz, whereas the answer key said: 75.7 Hz

I know how to solve part B because wavelength= velocity/ frequency but i don't have the correct frequency.

I wasn;t sure whether 320 hertz was the frequency of the detector or the source, so I plugged it into both to solve for the other, but I never ended up getting

320 is the frequency of the source. Solving for the two frequencies and taking the difference using 340m/s for c I got a somewhat different answer than either yours or the key. Mine was slightly smaller than the keys.

Using the approximation that the shift delta F= -(Vel/c) x f where c= speed of sound.

I get very close to the key's answer. Wavelength is calculated using the formula c=f x lambda where f is the preceived frequency.

Ahh i see you used 320 for Fs.

The reason that you got a slightly different answer was because in my book velocity of sound is given as 343 m/s.

The reason I was confused originally is because in the problem it stated "characteristic frequency" so I automatically thought that to be the frequency of the detector, since that can change.

But thank you very much!

Your welcome. I took characteristic to mean that this was the horn's primary frequency. Usually they are made up of several frequencies but tht is completely beside the point.

BTW, I tried both 340 and 343 and couldn't get the keys answer for total frequency shift using the proper eqns, but who knows may have made a mistake. I believe the answer was in the 73-74 Hz range. Using the approximation I was able to get 75Hz.

## 1. What is the Doppler Effect?

The Doppler Effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source.

## 2. How does the Doppler Effect affect sound?

The Doppler Effect affects sound by causing a change in the perceived frequency of a sound wave. When the source of the sound is moving towards the observer, the frequency appears higher (higher pitch), and when the source is moving away, the frequency appears lower (lower pitch).

## 3. What causes the Doppler Effect to occur?

The Doppler Effect is caused by the relative motion between the observer and the source of the wave. It can occur with any type of wave, including sound, light, and water waves.

## 4. What are some real-world applications of the Doppler Effect?

The Doppler Effect has many practical applications, such as in radar technology, where it is used to measure the speed and direction of moving objects. It is also used in medical ultrasound to create images of internal organs and in astronomy to study the movement of celestial objects.

## 5. How is the Doppler Effect related to the redshift and blueshift of light?

The Doppler Effect is responsible for the redshift and blueshift of light, which is the change in wavelength of light due to the relative motion between the source of the light and the observer. When an object is moving away from the observer, the light appears to have a longer wavelength (redshifted), and when the object is moving towards the observer, the light appears to have a shorter wavelength (blueshifted).

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