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Two air columns of resonance appatus, 10...

Two air columns of resonance appatus, 100cm and 101 cm long give 17 beats in 20 second, when each is sounding its fundamental mode. Calculate the velocity of sound.

Text Solution

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17 beats are produced in 20 seconds. Therefore beat frequency =17/20
`l_1`=1.0 and `l_2`=1.01 m , Now, `n_1=V/(4l_1), n_2=V/(4l_2)` Given that one end is closed
`rArr (n_1-n_2)=V/4 (1/l_1-1/l_2)`
`=V/4 ((l_2-l_1)/(l_1l_2))`
or `V=(4(n_1-n_2)(l_1-l_2))/((l_1-l_2))`
`=4xx17/20xx(1)(1.01)xx1/0.01` = 343.4 m/s
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