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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?

Text Solution

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The correct Answer is:
172.7
`200=(1)/(4l)sqrt((7//5RT)/(0.032))`, for the mixture, `f_("mix")=((2xx5)+(3xx6))/(2+3)=28//5`
`implies gamma_("mix")=1+(2)/(f_("mix"))=(19)/(14) implies f=(1)/(4l)sqrt((19//14RT)/(0.0416))`
`M_("mix")=((2xx32)+(3xx48))/(2+3)=41.6gm//mol=0.0416 kg//mol`
`implies (f)/(200)=sqrt((19xx0.2xx0.032xx5)/(14xx0.0416xx7))implies f=172.7Hz`.
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