# Doppler effect train frequency question

• Yoruichi
In summary: Keep in mind that the Doppler effect is only applicable for objects moving relative to each other. So when the train is approaching the crossing, the source (siren) and the detector (passenger) are moving toward each other, which results in a higher detected frequency. When the train moves away from the crossing, the source and detector are moving away from each other, resulting in a lower detected frequency. The key is to determine which is the source and which is the detector in each scenario. Great job on your summary!
Yoruichi

## Homework Statement

When a train running at a speed of 72 km/h approaches a crossing signal, a passenger in the train hears the siren at 720 Hz. What frequency does the passenger detect after the train passes the crossing signal? Take the speed of sound in air to be 340 m/s.

Doppler effect

## The Attempt at a Solution

First I convert the speed of train from 72 km/h into 20 m/s.
Speed of detector = 20 m/s
Speed of source = 0
Speed of sound = 340 m/s
Frequency of source = 720 Hz
Frequency of detector = ?

Using Doppler effect formula:

Fd = (340 - 20) / 340 x 720 (Since the detector is moving away from source, we want to make the denominator greater)
Fd = 677.64 Hz

But this isn't the answer. (The answer is 640 Hz)
May I know which part of my attempt goes wrong?

Hello,

At first the train is approaching the crossing. So what the passenger hears is not the frequency of the siren ...

At first, the train is moving toward the source, so the detected frequency is shifted higher. Is 720 Hz the source frequency or the detected frequency?

When the train moves away from the source, the frequency detected by the train will be lower than the source. Use the true source frequency to compute the detected frequency in this case.

BvU said:
Hello,

At first the train is approaching the crossing. So what the passenger hears is not the frequency of the siren ...

Dr. Courtney said:
At first, the train is moving toward the source, so the detected frequency is shifted higher. Is 720 Hz the source frequency or the detected frequency?

When the train moves away from the source, the frequency detected by the train will be lower than the source. Use the true source frequency to compute the detected frequency in this case.

Oh I see! So the 720 Hz is actually detected frequency instead of source frequency..
Therefore I have to divide my solution into two parts, which is to find out the frequency of detector first, and then only continue with my attempt above!

720 Hz = (340 + 20) / 340 x Fs
Fs = 720 x 340/360
= 680 Hz

Fd = (340 - 20) / 340 x 680
= 640 Hz

Thanks for the clarification!

Well done!

## 1. How does the Doppler effect affect the frequency of a train?

The Doppler effect is a phenomenon where the frequency of a wave appears to change when the source of the wave is in motion relative to the observer. In the case of a train, as the train approaches the observer, the sound waves are compressed and the frequency appears to increase. As the train moves away, the sound waves are stretched and the frequency appears to decrease.

## 2. What factors can affect the Doppler effect on a train?

The Doppler effect on a train can be affected by the speed of the train, the speed of sound, and the distance between the train and the observer. Additionally, the frequency of the train's sound, the direction of the train's motion, and any obstructions between the train and the observer can also impact the observed frequency.

## 3. How can the Doppler effect be used to measure the speed of a train?

The observed change in frequency due to the Doppler effect can be used to calculate the speed of a train. By measuring the change in frequency and knowing the speed of sound, the speed of the train can be determined using the formula v = fλ, where v is the speed, f is the frequency, and λ is the wavelength of the sound wave.

## 4. Can the Doppler effect also be observed for other types of waves besides sound waves?

Yes, the Doppler effect can be observed for any type of wave, including light waves. This effect is commonly seen in astronomy when measuring the speed and distance of celestial objects.

## 5. How does the Doppler effect on a train differ from the Doppler effect on a car?

The Doppler effect on a train is similar to the Doppler effect on a car, as both involve a moving source of sound. However, the speed and size of the train and the car can impact the observed frequency. Additionally, the shape and size of the train and car can also affect the sound waves and the resulting Doppler effect.

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