Beat frequency and velocity of observer

In summary: And that is the key to solving the problem....And that is the key to solving the problem.RainMD, we need to get back to solving the problem. The above was just a diversion to get you to understand the standing wave model for this problem.When you walk from one source to the other, how far will you have walked when you first hear a beat?RainMD, we need to get back to solving the problem. The above was just a diversion to get you to understand the standing wave model for this problem.When you walk from one source to the other, how far will you have walked when you first hear a beat?In summary, the question is asking for the velocity of the observer as they move
  • #1
RainMD
7
0

Homework Statement


Two sound sources 15m apart producing identical 229 Hz sounds. As you move from one to the other, you hear beat frequency of 2.5. How fast are you moving?[/B]

Homework Equations


The question asks for the velocity of the observer Vo. The trick here is to use the standing wave model to get the solution, NOT the doppler reflection equation.

The Attempt at a Solution


I used the doppler reflection equation to get a speed of 1.87 m/s. This was to see if my answer is wrong or right.
I started by getting the different frequencies from the beat equation (assuming one is 229 and the other is below/higher than that), and then I got the wavelengths. I solved for the change in wavelengths and divided that by the reciprocal of the beat frequency (time) to get a velocity of 0.4 m/s. Any ideas what I'm doing wrong?
 
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  • #2
Hello RainMD. Welcome to PF!

Which source has the Doppler shift? Or would both have a shift?
 
  • #3
TSny said:
Hello RainMD. Welcome to PF!

Which source has the Doppler shift? Or would both have a shift?
The question didn't specify, so I assumed both have doppler shift and solved for the correct velocity. Keep in mind that the question asks for the velocity using the standing wave model.
 
  • #4
OK, both sources will have a frequency shift. (In your first post it appears to me that you assumed only one of the sources is detected to have a shift in frequency.)

I don't get an answer of 0.4 m/s. I get the 1.87 m/s. If you'll show the details of your calculation, we can check your work.
 
  • #5
TSny said:
OK, both sources will have a frequency shift. (In your first post it appears to me that you assumed only one of the sources is detected to have a shift in frequency.)

I don't get an answer of 0.4 m/s. I get the 1.87 m/s. If you'll show the details of your calculation, we can check your work.
Okay, so I went with both sources shifting. That means f2= 230.25 and f1= 227.75 (in order to get 2.5 as the result of their differences)
Now I get the wavelength using the speed equation y = V/f , with v = 343 m/s (speed of sound). So 343/230.25 = 1.506
Same with the second frequency, 343/227.75 = 1.48.
So, the change in wavelength is 0.02 m. Is this correct?
 
  • #6
stts
RainMD said:
Okay, so I went with both sources shifting. That means f2= 230.25 and f1= 227.75 (in order to get 2.5 as the result of their differences)
Now I get the wavelength using the speed equation y = V/f , with v = 343 m/s (speed of sound). So 343/230.25 = 1.506
Same with the second frequency, 343/227.75 = 1.48.
So, the change in wavelength is 0.02 m. Is this correct?

If you walk between the sources you will not observe any change in wavelengths of the waves, but you will observe frequency shifts of the two individual waves.

But, this is kind of beside the point. You are asked to use a standing wave model rather than using the Doppler effect. So, we need to be clear about how to look at the problem from the point of view of a standing wave. As the two waves from the sources interfere in the region between the sources a standing wave is produced. The standing wave forms a stationary pattern relative to the ground (i.e., the nodes and antinodes are at fixed locations relative to the ground.)

As you walk between the sources, you are walking relative to the standing wave. Do you see why you will hear beats as you walk?
 
  • #7
TSny said:
tts

If you walk between the sources you will not observe any change in wavelengths of the waves, but you will observe frequency shifts of the two individual waves.

But, this is kind of beside the point. You are asked to use a standing wave model rather than using the Doppler effect. So, we need to be clear about how to look at the problem from the point of view of a standing wave. As the two waves from the sources interfere in the region between the sources a standing wave is produced. The standing wave forms a stationary pattern relative to the ground (i.e., the nodes and antinode are at fixed locations relative to the ground.)

As you walk between the sources, you are walking relative to the standing wave. Do you see why you will hear beats as you walk?

So, the beats represent a relationship between nodes and antinodes? Since I'm walking from a high frequency to a lower one? I don't get how this will help since beats are just a difference.
 
  • #8
As you walk along the standing wave, what will you hear at the instant you pass a node? An antinode?
 
  • #9
TSny said:
As you walk along the standing wave, what will you hear at the instant you pass a node? An antinode?

Antinodes = high pitch sound
Nodes = low or normal pitch sounds
Is that correct?
 
  • #10
No. You will hear essentially only one pitch. But what about the loudness of that pitch when you are at a node? An antinode?
 
  • #11
TSny said:
No. You will hear essentially only one pitch. But what about the loudness of that pitch when you are at a node? An antinode?

A loud pitch at antinodes and a low one in nodes, since they represent constructive and destructive interference point (?)
I'm really sorry about all the confusion I'm causing.
 
  • #12
"Pitch" refers to frequency. As you walk along the standing wave, you do not hear any change in frequency. But you are right that at the antinodes the sound will be loud while at the nodes the sound will be soft. (Ideally, there would be no sound at the nodes.) So, as you walk along the standing wave and go from node to anti-node to node to anti-node to...etc. you will hear soft, loud, soft, loud, ...etc. Beats! How often you hear beats depends on how fast you are walking. So, there should be a way to deduce your speed of walking from the given beat frequency. But, you'll need to know the distance between the nodes or antinodes.
 
Last edited:
  • #13
TSny said:
"Pitch" refers to frequency. As you walk along the standing wave, you do not hear any change in frequency. But you are right that at the antinodes the sound will be loud while at the nodes the sound will be soft. (Ideally, there would be no sound at the nodes.) So, as you walk along the standing wave and go from node to anti-node to node to anti-node to...etc. you will hear soft, loud, soft, loud, ...etc. Beats! How often you hear beats depends on how fast you are walking. So, there should be a way to deduce your speed of walking from the given beat frequency. But, you'll need to know the distance between the nodes or antinodes.

Thank you so much! I solved the problem with your help. Have a great day!
 
  • #14
Great!
 

1. What is the beat frequency?

The beat frequency is the difference between the frequencies of two sound waves that are interfering with each other. It is measured in hertz (Hz) and can be calculated by subtracting the lower frequency from the higher frequency.

2. How does the velocity of the observer affect the beat frequency?

The velocity of the observer does not directly affect the beat frequency. However, if the observer is moving towards or away from the source of the sound waves, the frequency of the waves will appear to change, resulting in a change in the beat frequency.

3. What is the relationship between beat frequency and velocity of the source?

The beat frequency is directly proportional to the velocity of the source. This means that as the velocity of the source increases, the beat frequency also increases.

4. How is the beat frequency affected by the distance between the source and the observer?

The beat frequency is not affected by the distance between the source and the observer. However, as the distance increases, the intensity of the sound waves decreases, which can affect the perceived beat frequency.

5. Can the beat frequency be heard by the human ear?

Yes, the beat frequency can be heard by the human ear. It can be perceived as a pulsating sound when two sound waves with slightly different frequencies interfere with each other. The frequency range that is audible to humans is between 20 Hz and 20,000 Hz.

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