Question

Assertion :Fundamental frequency of a narrow pipe is more. Reason: According to Laplace end correction if radius of pipe is less, frequency should be more.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Let speed of sound be $v$.

Also $L$ and $r$ be the length and radius of the pipe respectively.

Fundamental frequency of a pipe (say closed organ pipe) $\nu =\frac{v}{4(L+e)}$ where $e=0.6r$ is the end correction.

Thus $\nu =\frac{v}{4(L+0.6r)}$ which implies frequency increases due to decrease in radius of the pipe.

Hence Reason explains the Assertion very well.