The fundamental frequency of an open organ pipe is 300Hz. The first overtone of this has same frequency as that of first overtone of a closed organ pipe. If speed of sound is 330m/s, then the length of closed of organ pipe will be

Options

A. 41 cm
B. 37 cm
C. 31 cm
D. 80 cm

Answer

C

Explanation

For an open pipe, fundamental frequency `upsilon=(v)/(2L)`
`therefore L=(v)/(2upsilon)=(330)/(2xx300)=(11)/(20)`
As frequency of `1^(st)` overtone of open pipe
= frequency of `1^(st)` overtone of closed pipe `therefore (2v)/(2L)=(3v)/(4L)`
or `L=(3L)/(4)=(3)/(4)xx(11)/(20)=0.4125m=41.25cm~~41cm`