Waves and Sound: Find Moving Train Speed

In summary, the problem involves two train whistles with frequencies of 180 Hz in air and one train approaching the station. A beat frequency of 2 Hz is heard from the moving train's whistle. Using the equation fbeat = |fo - fs|, we can calculate fo (observer frequency) by adding the beat frequency (2 Hz) to the source frequency (180 Hz). Then, using the equation fo = fs (v + vo / v - vs) and rearranging it to isolate vs, we can solve for the speed of the moving train. The first step is to multiply both sides by (v - vs) and the next step would be to distribute the fs to the terms inside the parentheses.
  • #1
harujina
77
1

Homework Statement



Two train whistles have frequencies of 180 Hz in air (v = 344 m/s). When one train is at rest sounding its whistle, a beat frequency of 2 Hz is heard from the moving train which is sounding its whistle as well. What is the moving train's speed if it is approaching the station?

Homework Equations



fbeat = l fo - f1 l

fo = fs (v + vo / v - vs) ; [source is approaching the observer]

fo: observer
fs: source

The Attempt at a Solution



v = 344 m/s
fs = 180 Hz
fo = 182 Hz [fo = fbeat + fs; = 2 Hz + 180 Hz]
vo = 0
vs = ?

fo = fs (v + vo / v - vs) ; [source is approaching the observer]

I'm trying to rearrange this formula to isolate vs but for some reason I can't.
Where do I start... I've tried everything. :confused:

And sorry about all the questions, I'm having some significant trouble with this unit in physics...
 
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  • #2
The first step is to multiply both sides by (v - vs). Can you see why? What is the next step?
 

1. How do waves and sound help us determine the speed of a moving train?

Waves and sound are useful tools for measuring the speed of a moving train because they can be easily detected and measured. As the train moves, it creates sound waves that travel through the air. By measuring the frequency and wavelength of these sound waves, we can calculate the speed of the train.

2. What is the relationship between the speed of a moving train and the frequency of sound waves it produces?

The frequency of sound waves is directly proportional to the speed of a moving train. This means that as the train's speed increases, the frequency of the sound waves it produces also increases. Similarly, as the train's speed decreases, the frequency of the sound waves decreases as well.

3. Can other factors affect the accuracy of using waves and sound to find a train's speed?

Yes, there are other factors that can affect the accuracy of using waves and sound to find a train's speed. These include wind, temperature, and the direction of the train's movement. These factors can cause variations in the sound waves, making it important to take them into account when making calculations.

4. Are there any limitations to using waves and sound to find a train's speed?

While waves and sound can provide accurate measurements of a train's speed, there are limitations to this method. For example, if the train is moving too fast, the sound waves it produces may become distorted, making it difficult to accurately measure their frequency and wavelength. Additionally, if there are obstructions or barriers between the train and the measuring device, this can also affect the accuracy of the results.

5. How can waves and sound be used to find the speed of a train without being in close proximity to it?

Waves and sound can be used to find the speed of a train from a distance by using specialized equipment such as Doppler radar or laser speed guns. These devices use the Doppler effect to measure the frequency of the sound waves reflecting off the train and calculate its speed. This method is commonly used by law enforcement to track the speed of moving vehicles on highways.

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