Question

The first overtone of an open orgen pipe beats with the first ouertone of a closed orgen pipe with a beat frequency of `2.2 H_(Z)` . The fundamental frequency of the closed organ pipe is `110 H_(Z)` . Find the lengths of the pipes . Speed of sound in air `u = 330 m//s` .

Answer 1

Fundamental frequecy of closed organ pipe
`v_(c)=(upsilon)/(4L_(c)) :. L_(c)=(upsilon)/(4v_(c))=(330)/(4xx110)=0.75m`
Frequency of first overtone of open organ pipe `v_(1)=2xx(upsilon)/(2L_(0))=(upsilon)/(L_(0))`
Frequency of first overtone of closed organ pipe `v_(2)=3xxv_(c)=(3upsilon)/(4L_(0))=(3xx330)/(4xx0.75)=330Hz`
As, `v_(1)-v_(2)=2.2Hz :. (upsilon)/(L_(0))-330=2.2 or (upsilon)/(L_(0))=332.2`
`L_(0)=(upsilon)/(332.2)=(330)/(332.2)m=0.003m =99.3cm`