Two organ pipes are identical except that one is filled with oxygen and other with a mixture of oxgen and nitrogen. The temperature and total pressure in each pipe are the same when two are sounded together a note of `440 Hz` is heard, which beats one every second. What is the percentage partial pressure of the nitrogen in the mixture ? Assume that the molecular weight of oxygen is `32` and of nitrogen `28`, and their principal specific heats are identical.

Answer

`3.6%`

Explanation

The pipe with nitrogen has lower density, higher speed of sound and `:.` high frequency
So let frequency be `440, 441 Hz` as shown ltbr. `O_(2) , 440`
`O_(2) + N_(2) , 441`

Since `c = sqrt((gammaP)/(rho)) = lambdaf` and `p x` molecular weight
we can write `(f_(1))/(f_(2)) = sqrt((r_(2))/(r_(2))) = sqrt((32(1-n)+28n)/(32))`
where `n =` fraction of `N_(2)`.
`(8 - n)/(8) = ((440)/(441))^(2)`
giving `n = 0.03624` or `3.6%`