Two closed pipes have the same fundamental fr | vedclass

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(A) The fundamental frequency of a closed pipe is given by $f = \frac{v}{4l}$,where $v$ is the speed of sound in the gas and $l$ is the length of the

Vedclass · Accepted Answer

$1:4$

Vedclass · Answer

(A) The fundamental frequency of a closed pipe is given by $f = \frac{v}{4l}$,where $v$ is the speed of sound in the gas and $l$ is the length of the pipe.Since $v = \sqrt{\frac{\gamma RT}{M}}$,we have $f = \frac{1}{4l} \sqrt{\frac{\gamma RT}{M}}$.Given that the fundamental frequency $f$ and temperature $T$ are the same for both pipes,we have $l \propto \frac{1}{\sqrt{M}}$,where $M$ is the molar mass of the gas.For oxygen $(O_2)$,$M_1 = 32 \ g/mol$. For hydrogen $(H_2)$,$M_2 = 2 \ g/mol$.The ratio of their lengths is $\frac{l_1}{l_2} = \sqrt{\frac{M_2}{M_1}} = \sqrt{\frac{2}{32}} = \sqrt{\frac{1}{16}} = \frac{1}{4}$.Thus,the ratio of their lengths is $1:4$.

Two closed pipes have the same fundamental frequency. One is filled with oxygen and the other with hydrogen at the same temperature. The ratio of their lengths respectively is

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