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A closed organ pipe resonates in its fun...

A closed organ pipe resonates in its fundamental mode at a frequency of `200 H_(Z)` with `O_(2)` in the pipe at a certain temperature. If the pipe now contains `2` moles of `O_(2)` and `3` moles of ozone, then what will be fundamental frequency of same pipe at same temperature?

A

`268.23 H_(Z)`

B

`175.4 H_(Z)`

C

`149.45 H_(Z)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`M = (n_(1) M_(1) + n_(2) M_(2))/( n_(1) + n_(2))`
`= ((2) (32) + (3) (48))/(5) = 41.6`
`f = (nu)/(4l)` or `f prop nu`
But, `nu = sqrt((gammaRT)/(M))`
or `nu prop (1)/sqrt(M)`
:. `f prop (1)/sqrt(M)`
:. `(f_(2))/(f_(1)) = sqrt((M_(1))/(M_(2)))`
or `f_(2) = (sqrt((M_(1))/(M_(2)))) f_(1)`
`= (sqrt((32)/(48))) (200) = 175.4 H_(Z)`
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