What are the Water Heights for a Standing Wave in a Tuning Fork and Tube Setup?

[kmoukiss]

Homework Statement

A 1.0m long vertical tube is filled with water. A tuning fork vibrating at 580Hz is held over the open top of the tube as the water is slowly drained from the bottom. At what water heights, measured from the bottom of the tube, will there be a standing wave in the tube?
Speed of sound in air =340m/s

Homework Equations

For an open-open tube: fn=n*v/2*L
For an open-closed tube: fn=n*v/4*L

The Attempt at a Solution

I don't know if this is an open open or an open closed tube...
What I have done is : If there was no water, its open open, then fundamental frequency is fn=340/2=170Hz

Now we drain water, it becomes open-closed and we want to find the length of the tube which remains with no water in it AT THE MOMENT there is a standing waves.

So L(prime)=V/4fn, fn is the one calculated before. L(prime)= 0.5m

But I don't know if i can re use fn as I did orI am correct in all that!

Please help me ! Thank you.

 

[Doc Al]

Think of the surface of the water as the (closed) bottom of the tube of air.

 

[kmoukiss]

Yes that is exactly what i thought! so the "demonstration" I have made above, is it correct ? I mean can i first calculate the fundamental frequency as i did to r-plug it into the final formula ?

Thank you!

 

[Doc Al]

Answer this: What's the wavelength of the sound? For what lengths of air column will there be a standing wave in the open-closed air column?

 

[kmoukiss]

But do I work out the wavelenght of this sound using lamda=f*v . I guess yes.

And then I use this wavelenght in lamda=4L/n?
I mean, how do i use the wavelength then ? I need to find several lenghts no ?

Thank you so much.

 

[Doc Al]

But do I work out the wavelenght of this sound using lamda=f*v .

The wave relationship is: v = lambda*f. Use that to solve for lambda.

Then draw yourself a diagram of the first several standing wave patterns in the tube. What's the shortest column that can support a standing wave? The next shortest? Etc.

 

[Doc Al]

You may find this helpful: http://www.physicsclassroom.com/Class/sound/U11L5d.cfm"

 

[kmoukiss]

Thank you.

But I need to don't randomly draw thoses sketchs right ?
How do I do ? :(
I really don't understand the point... (NOT your fault at all! just mine !)

 

[Doc Al]

Read the link I posted. It shows the first few standing waves.

 

[kmoukiss]

I have drawn the first 3 ... but why do I need to draw them ? :$

 

[Doc Al]

The only purpose of drawing the standing waves is to help you determine the column lengths. That's what you need to find. So, in terms of the wavelength, what are the first three air column lengths that produce standing waves?

 

[kmoukiss]

So the first three harmonics are the first, the third and the fifth (odd numbers).
And so the first lambda is = 4L
The third to 5/3*L
The fith to 4/5*L
Right ? :s

 

[Doc Al]

So the first three harmonics are the first, the third and the fifth (odd numbers).
And so the first lambda is = 4L
The third to 5/3*L
The fith to 4/5*L
Right ? :s

Not exactly. Realize that lambda is given (or at least you can calculate it). You are trying to find the column lengths.

The first standing wave pattern: L = lambda/4

The second: L = lambda/2 + lambda/4 = (3/4)lambda

And so on...

 

[kmoukiss]

So those means that there are several "L" for which there is a standing waves...
I thought I had to use formulas... :( It would be more simple for me i think but I have understood the procedure thanks to you!

 

[kmoukiss]

The lambda is given... ? you mean one "full" circle = lambda/2 ...?

 

[Doc Al]

So those means that there are several "L" for which there is a standing waves...

Yes. This is a bit trickier than the standard problem where the column length is fixed and you are solving for the wavelength/frequency of the harmonics. In this problem, the wavelength/frequency is given and you have to find the various column lengths.

The lambda is given... ?

I mean that you can calculate the wavelength from the given speed and frequency. See post #6.

 

[kmoukiss]

But so Lambda stay the same... but varying the coefficient, leads to vary the L, right ?