Question

A closed pipe has certain frequency. Now its length is halved. Considering the end correction, its frequency will now become

• A. Double
• B. More than double
• C. Less than double
• D. Four times

Answer 1

Answer: (C)

Less than double

For a closed pipe,

$f_n=\frac{(2n-1)v}{4(L+D)}$,

where, $f_n$ is the frequency, $n=$ integer, $v=$ velocity; $L=$length of the pipe and $D=$ diameter of the pipe.

When length is halved, the frequency becomes, $f_n^{\prime }=\frac{(2n-1)v}{4\left[\right(L/2)+D)]}$

Comparing these two equations, we can say frequency will become little less than double.