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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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Knowledge Check

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

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

  • 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

    A
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    B
    `332ms^(-1)`
    C
    `323.2ms^(-1)`
    D
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  • If the two tubes of lengths 50cm and 51cm closed at one end produce 7 beats in two second, when sounded to their fundamental notes neglecting end correction , then velocity of sound in air will be

    A
    350m/s
    B
    352m/s
    C
    354m/s
    D
    357m/s

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