Close tube with string oscillation

In summary, the tube oscillates at its fundamental frequency when the string is plucked between points a-e.
  • #1
IIK*JII
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Homework Statement


In attached figure, a closed tube is placed near a string that is fixed at one end and has a weight attached to its other end. When bridges A and B are positioned at the points shown,plucking the string between A and B causes the tube to resonate at its fundamental frequency. Points a-e divide the length between A and B into 6 equal segments

Next, A is fixed in place, and B is gradually moved toward A while the closed tube is shifted so that it stays at the center of A and B. During this process, the string is repeatedly plucked between A and B. When B is at a certain point, the tube resonates at the next overtone above the fundamental frequency. Which of a-e represents that point? Here, the string's oscillation is only fundamental oscillation


Homework Equations


Close tube; L= (2n-1)[itex]\frac{λ}{4}[/itex] ; n= 1,2,3...
String fixed end; λ=2L/n

The Attempt at a Solution


In 2nd period the tube oscillate at f3

L = [itex]\frac{3}{4}[/itex]λ
∴λtube=[itex]\frac{4}{3}[/itex]L ...(1)
String ; λstring=2L (oscillate at f1) ...(2)

Divide (1)/(2) I got [itex]\frac{λtube}{λstring}[/itex] = 2/3

From that I guess the point is a point number 2 from first 3 points, so I don't know that I should choose point b or d as my answer. Also, I don't know that my method is correct or not...

Help is appreciated :)
Thanks
 

Attachments

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  • #2
The question is not how much you have to reduce the entire wavelength on the string but how far to move the blocks ...
 
  • #3
Thank you very much Simon Bridge :)
Did you mean the block should move up?? and I should find height of the block when it moves up??
 
  • #4
What I am saying is that you have calculated a ratio in whole wavelengths, but the distance you need to find (in order to know where to put the block) is that for a half-wavelength. You need to check to see what sort of difference, if any, that makes.

Presumably, the ratio of the fundamental to the first harmonic in the tube is the ratio of string wavelengths needed right? You already know the half-wavelength needed to make the string oscillate at the tube's fundamental frequency and you are keeping the tension, and so the wave-speed, fixed.

I hope I'm not confusing you - it is really hard to write about without actually telling you the answer. Basically the numbers you got look good - I'm trying to get you to work out if the numbers you got are the ones you need ... what you really need is a relationship along the lines of [itex]x_2=ax_1[/itex] where x1 is the distance |AB| that got you the fundamental in the tube and x2 is the distance between the blocks that gets you the second fundamental and a is the ratio between them.[1]

What you have is that [itex]\lambda_{tube} = \frac{2}{3}\lambda_{string}[/itex]

----------------------
[1] actually you can finesse it by looking for the relation [itex]x_2=\frac{n}{6}x_1[/itex] since n will tell you which of the lettered points to move the block to :)
 
  • #5
Thank you Simon Bridge,,
your explanation is good help me imagine what this problem want

I think, for example, x2 from your meaning is length of string that I can find from wavelength right??
 
  • #6
Bear in mind that I think you are very close and I have not actually done the problem myself. It's intreguing - I'll have to set it up as an experiment sometime.
 
  • #7
:))
Thank you Simon Bridge
I got it now :)
 
  • #8
Cool: well done :)
 

1. What is a "Close tube with string oscillation" experiment?

The "Close tube with string oscillation" experiment is a physics demonstration that involves creating sound waves by oscillating a string that is attached to a closed tube. The sound waves travel through the air inside the tube and create a resonant frequency that can be heard as a distinct pitch.

2. How is the experiment set up?

To set up the "Close tube with string oscillation" experiment, you will need a closed tube (such as a cardboard tube or PVC pipe), a string, a rubber band, and a weight (such as a washer or paperclip). Attach one end of the string to the closed tube using the rubber band, and tie the other end of the string to the weight. Make sure the string is taut and the weight can swing freely. You can also attach a ruler to the tube to measure the length of the string.

3. What factors affect the frequency of the sound produced?

The frequency of the sound produced in the "Close tube with string oscillation" experiment is affected by several factors, including the length of the string, the tension of the string, and the diameter of the closed tube. As the length of the string or the diameter of the tube is changed, the resonant frequency of the sound will also change.

4. How can I change the pitch of the sound produced?

To change the pitch of the sound produced in the "Close tube with string oscillation" experiment, you can adjust the length of the string or the diameter of the tube. Shortening the string or using a smaller diameter tube will increase the frequency and produce a higher pitch. Lengthening the string or using a larger diameter tube will decrease the frequency and produce a lower pitch.

5. What other factors may affect the results of the experiment?

Other factors that may affect the results of the "Close tube with string oscillation" experiment include the temperature and humidity of the air inside the tube, as well as any background noise or interference. It is important to conduct the experiment in a quiet environment and try to maintain a consistent temperature and humidity for reliable results.

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