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A closed air column 32 cm long is in res...

A closed air column `32 cm` long is in resonance with a tuning fork . Another open air column of length `66 cm` is in resonance with another tuning fork . If the two forks produce `8 beats//s` when sounded together , find
the speed of sound in the air

A

`33792 cm//s`

B

`35790 cm//s`

C

`31890 cm//s`

D

`40980 cm//s`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `c` be the speed of sound and `f_(1) , f_(2)` be the frequency of tuning forks.
`f_(1) = ( c )/(4 l_(1)) = ( c )/( 4 xx 32) = ( c )/( 128)`
`f_(2) = ( c )/( 2 l_(2)) = ( c )/( 2 xx 66 ) = ( c )/( 132)`
Now `| f_(1) - f_(2)| = 8`
As `f_(1) gt f_(2)` we have `| f_(1) - f_(2)| = 8`
`( c )/(128) - ( c )/( 132) = 8`
`c = (128 xx 132 xx 8)/(4) = 33792 cm//s`
`f_(1) = ( c )/( 128) = 264 Hz`
`f_(2) = ( c )/( 132) = 256 Hz`
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Knowledge Check

  • In a closed tube when air column is 20cm it is in resonance with tuning fork A. When the length is increased by 2cm then the air column is in resonance with tuning fork B. When A and B are sounded together they produce 8 beats per second . The frequencies of the tuning forks A and B are (in Hz)

    A
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    B
    `88,30`
    C
    `80,88`
    D
    `44,40`

  • A resonance air column of length 20 cm resonates with a tuning fork of frequency 250 Hz . The speed of sound in air is

    A
    `300 m//s`
    B
    `200 m//s`
    C
    `150 m//s`
    D
    `75 m//s`

  • A resonance occurs with a tuning fork and an air column of size 12 cm . The next higher resonance occurs with an air column of 38 cm . What is the frequency of the tuning fork ? Assume that the speed of sound is 312 m//s .

    A
    `500 Hz`
    B
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    C
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