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A cylindrical tube open at both ends, ha...

A cylindrical tube open at both ends, has a fundamental frequency `f` in air. The tube is dipped vertically in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now

A

`f//2`

B

`3f//4`

C

f

D

`2 f`

Text Solution

Verified by Experts

The correct Answer is:
C
Case I Here `lamda//2 = l`
`:. lamda = 2 l`
Now, `v = f xx lamda`
`:. f = (v)/(lamda) = (v)/(2 l)` ….(i)
Case II Here `lamda'//4 = l//2`
`:. lamda' = 2 l`
Now, `v = f' xx lamda'`
`:. f' = (v)/(lamda') = (v)/(2l) = f`.
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Knowledge Check

  • A cylindrical tube, open at the both ends, has a fundamental frequency f in air . The tube is dipped vertically in water so that half of it is in water . The fundamental frequency of the air column is now-

    A
    `f//2`
    B
    `3f//4`
    C
    `f`
    D
    `2 f `

  • A pipe open at both ends has a fundamental frequency f in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now :

    A
    `(3f)/4`
    B
    2f
    C
    f
    D
    `f/2`

  • A pipe open at both ends has a fundamental frequency f in air. The pipe is dippoed vertically in water so that half of it is in water. The fundamental frequency of the air column is now :-

    A
    f
    B
    `(f)/(2)`
    C
    `(3f)/(4)`
    D
    2f
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