Question

An organ pipe of length $L$ open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of $480Hz$. What should be the length of a pipe closed at one end, so that it also vibrates in its first harmonic with the same tuning fork?

Answer 1

Given,

For an organ pipe of length $L$ open at both ends, fundamental frequency is given by

${\nu }_o=\frac{V}{{\lambda }_1}=\frac{V}{2L}=480Hz$…(i)

For closed pipe of same fundamental frequency, length should be $\left(L^{\prime }\right)$

${\nu }_o=\frac{V}{{\lambda }_2}=\frac{V}{4L\text{'}}$…(ii)

For constant $\lambda$ from (i) and (ii)

$L^{\prime }=\frac{L}{2}$



Final Answer: $\frac{L}{2}$ as $\lambda$ is constant