Question

An organ pipe of length K open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of 480 Hz. 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?

• A. $\frac{L}{4}$
• B. $\frac{L}{2}$
• C. L
• D. 2L

Answer 1

Answer: (B)

$\frac{L}{2}$

Answer 2

For open organ pipe, frequency of first harmonic,

$\upsilon = \frac{v}{2L} = 480Hz$

For a pipe closed at one end, frequency of first harmonic,

$\upsilon' = \frac{v}{2L} = 480Hz$

$\therefore 4L` = 2LorL' = \frac{2L}{4} = \frac{L}{2}$