Assertion : The fundamental frequency of an o | vedclass

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(A) The fundamental frequency $f$ of an open organ pipe of length $l$ is given by $f = \frac{v}{2l}$,where $v$ is the velocity of sound in the air col

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If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.

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(A) The fundamental frequency $f$ of an open organ pipe of length $l$ is given by $f = \frac{v}{2l}$,where $v$ is the velocity of sound in the air column.As the temperature $T$ increases,the velocity of sound $v$ increases according to the relation $v = \sqrt{\frac{\gamma RT}{M}}$.While the length $l$ of the pipe may increase slightly due to thermal expansion,the increase in the velocity of sound $v$ is much more significant.Since $f \propto v$ and $f \propto \frac{1}{l}$,the increase in $v$ dominates the effect of the slight increase in $l$,leading to an overall increase in the fundamental frequency $f$.Therefore,both the Assertion and the Reason are correct,and the Reason provides a correct explanation for the Assertion.

$Assertion :$ The fundamental frequency of an open organ pipe increases as the temperature is increased.
$Reason :$ As the temperature increases,the velocity of sound increases more rapidly than the length of the pipe.

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$Assertion :$ The fundamental frequency of an open organ pipe increases as the temperature is increased.$Reason :$ As the temperature increases,the velocity of sound increases more rapidly than the length of the pipe.