Standing Waves, Fundamental Frequency, etc

[G1SG2]

Page 346 of TPR Hyperlearning PS:

"...if one end of the tube is closed, that end will be a pressure antinode, while the open end will still be a pressure node. It turns out that in such a case the length of the tube L must be an ODD NUMBER of quarter-wavelengths in order for the tube to support a standing sound wave. As a result, f=nv/4L, and lamda=4L/n, where n is an ODD NUMBER. The same formulas would also apply to traverse standing waves on a rope if one end was fixed and the other end was allowed to oscillate freely."


So, if we have one end of the tube open, L AND n are always odd numbers???

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[thebillsfan]

Well, n is always an odd number. L is not necessarily even a whole number, let alone odd or even...L is however long the pipe-maker wants it to be.

 

[G1SG2]

Well, n is always an odd number. L is not necessarily even a whole number, let alone odd or even...L is however long the pipe-maker wants it to be.

Hmm. But TPR makes it sound like L has to be an odd number? "It turns out that in such a case the length of the tube L must be an ODD NUMBER of quarter-wavelengths in order for the tube to support a standing sound wave."

That confuses me.

 

[thebillsfan]

odd number of QUARTER WAVELENGTHS.

L is not dependent on lambda, rather lamdba is dep on L. Whatever L is, lambda will be related to that via the equation lambda=4L/n. Rearranging this we get lambda👎/4=L
Can you imagine a situaiton where lambda is an even number, such that if you multiply by an odd integer n and divide by four you'll come up with an even value for L? If so, you're thinking about this the right way.

Once again, L is NOT dependent on wavelength. a rough analogy is that it's like how velocity of sound in a medium is not dependent on wavelength, but instead a property of the medium itself.

 

[inaccensa]

Page 346 of TPR Hyperlearning PS:

"...if one end of the tube is closed, that end will be a pressure antinode, while the open end will still be a pressure node. It turns out that in such a case the length of the tube L must be an ODD NUMBER of quarter-wavelengths in order for the tube to support a standing sound wave. As a result, f=nv/4L, and lamda=4L/n, where n is an ODD NUMBER. The same formulas would also apply to traverse standing waves on a rope if one end was fixed and the other end was allowed to oscillate freely."


So, if we have one end of the tube open, L AND n are always odd numbers???

I thought the end that was closed was the node and the open end was the antinode in a wave. Is it different for pressure

 

[matth87]

If one end is open (pressure node) and one end is closed (antinode) use the following formula

L = 👎 x (1/4) x (wavelength)
n = 1,3,5,7,9.... any odd number

L = length
n = harmonic number
wavelength = nth wavelength

Where you having trouble pookie is you need to bold your text a little bit more.

L must be an ODD NUMBER of quarter-wavelengths
this "odd number of quater-wavelengths" is equal to n
L = 👎 x (quater-wavelength)
n = odd number
quater-wavelength = (1/4 x wavelength)