An open organ pipe has a fundamental frequency of `300 H_(Z)` . The first overtone of a closed organ pipe has the same frequency as the first overtone of this open pipe . How long is each pipe ? (Speed of sound in air = `330 m//s`)

Options

A. `10 cm`
B. `41 cm`
C. `82 cm`
D. `164 cm`

Answer

B

Explanation

For open organ pipe `n=(v)/(2l_1)=300`
First overtone of open organ pipe
`=2((v)/(4l_2))=2xx300=600Hz`
First overtone of closed organ pipe
`=3((v)/(4l_2))`
Given `3((v)/(4l_2))=600impliesl_2=(v)/(800)=(330)/(800)m`
`=0.41m`