# 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

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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

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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)