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 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 ?

An organ pipe of length L open at both ends is found to vibrate in its

1.	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 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 ?
Answer» Solution :Initially, first HARMONIC of open pipe is equal to 480 Hz. Hence `(V)/(2L) =480 ""…(1)` (Where v = volocity of SOUND in air) Finally, first harmonic of CLOSED pipe is equal to 480 Hz. Hence, `(v)/(4L)=480""…(2)` From `(v)/(2L) = (v)/(2L) implies L. = (L)/(2)`