# Waves in a closed organ pipe (homework check)

• Sullo
In summary: The variable names are already different, so it would be redundant to use different variable names. It would also make the work more complicated and difficult to follow.

## Homework Statement

A closed organ pipe of length 1.00m is filled with a gas and is found to give the same note as an open pipe of length 1.30m filled with air, when both are resonating at their fundamental mode of vibration

a) draw diagrams to show the nature of the waves in each pipe and use them to assist in your working
b) find the ratio of the velocity of sound in the gas compared to the velocity of sound in air.

b)
f(open) = v/2L
f(closed) = v/4L

## The Attempt at a Solution

a) The diagrams I've drawn look like this:

open:
https://imgur.com/a/MXcmJ5h closed: https://imgur.com/a/cK79JjL

b)
f(open) = v/2L
v = 1/2Lf
-> 1/2(1.30)f
=1/2.60f

f(closed) = v/4L
v = 1/4Lf
v = 1/4(1.00)f
v = 1/4.00f

ratio = vclosed/vopen

= (1/4.00f) / (1/2.60f)
= 2.60f/4.00f
= 2.60/4.00 (f cancels, same pitch)
= 0.650

#### Attachments

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Sullo said:
b)
f(open) = v/2L
v = 1/2Lf
-> 1/2(1.30)f
=1/2.60f

f(closed) = v/4L
v = 1/4Lf
v = 1/4(1.00)f
v = 1/4.00f
Check your algebra for both: you've made the same mistake rearranging the expressions to solve for v in each case.

gneill said:
Check your algebra for both: you've made the same mistake rearranging the expressions to solve for v in each case.
Thank you for pointing this out.

So it should be v = 2lf v = 4lf ?

Sullo said:
Thank you for pointing this out.

So it should be v = 2lf v = 4lf ?
Yes.

I might also suggest that you alter the variable names to distinguish the two cases right from the start. This can help prevent mistakenly combining or cancelling variables that really are different when you work the algebra (Not that you've done this here, I'm just saying for future work where the equations might be more complicated). It will also make your work more clear and easy to follow for others.

It's clear that there are two different lengths and velocities involved in the problem, one for the open pipe and one for the closed pipe. Why not write them as ##L_o## and ##v_o##, and ##L_c## and ##v_c## for example?

## 1. What is a closed organ pipe?

A closed organ pipe is a hollow cylindrical tube that is sealed at one end and open at the other end. It is used to produce musical notes in pipe organs and other wind instruments.

## 2. How do waves travel in a closed organ pipe?

In a closed organ pipe, sound waves travel as longitudinal waves, meaning they move parallel to the direction of the wave. These waves are caused by vibrations in the air inside the pipe, which are produced by the air being blown into the pipe.

## 3. What factors affect the wavelength of waves in a closed organ pipe?

The wavelength of waves in a closed organ pipe is affected by the length of the pipe, the speed of sound in the air, and the frequency of the sound waves. The longer the pipe, the longer the wavelength. The faster the speed of sound, the shorter the wavelength. And the higher the frequency, the shorter the wavelength.

## 4. How is the frequency of waves in a closed organ pipe determined?

The frequency of waves in a closed organ pipe is determined by the length of the pipe and the speed of sound in the air. The frequency can be calculated using the formula f = nv/2L, where f is the frequency, n is the number of nodes (points of zero displacement) in the pipe, v is the speed of sound, and L is the length of the pipe.

## 5. Can you have multiple wavelengths in a closed organ pipe?

No, a closed organ pipe can only have one wavelength at a time. This is because the pipe is a closed system, meaning the air inside is not free to move in all directions. Therefore, only one wavelength can fit inside the pipe at a time.

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