Two closed organ pipes of length 100 cm and 101 cm 16 beats is 20 sec. When each pipe is sounded in its fundamental mode calculate the velocity of sound `

Options

A. `303 ms^(-1)`
B. `332 ms^(-1)`
C. `323.2 ms^(-1)`
D. `300 ms^(-1)`

Answer

c

Explanation

Let / be the length of pipe and v is the veloctiy of
sound, then the frequency of note emitted from the pipe is
`n v/(4l)`

Number of beats in 1s` = 16/20=4/5`
For a closed organ pipe, `x=n_(1) - n_(2) = v/4 (1/l_(1)-1/l_(2))`
`4/5 = v/4 (1/1-1/(1.01))=(0.01v)/(4xx1xx1.01)`
`rArr 0.01 xx 5 v=16xx 1.01`
` therefore v=(16xx1.01)/(0.05) = 323.2ms^(-1)`