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## 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.

## Homework Equations

b)

f(open) = v/2L

f(closed) = v/4L

## The Attempt at a Solution

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

open:

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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