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A tuning fork of frequency 340 Hz is exc...

A tuning fork of frequency `340 Hz` is excited and held above a cylindrical tube of length `120 cm`. It is slowly filled with water. The minimum height of water column required for resonance to be first heard( Velocity of sound `=340 ms^-1`) is.

Text Solution

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Here , the tunning fork vibrates in resonance with the air column in the pipe closed at one end . The resonant frequency of the air column is given by
` f = (nv)/( 4l) where n = 1 , 2 , 3 , …`
The length of the air column is given by
` l = (nv)/( 4f) = ( n (340))/( 4(340)) = 0.25 n m = 25 n cm`
` l = 25 cm , 75 cm , 125 cm `
Since the length of the tube is `120 cm`, therefore , the possible lengths of air column are
` l = 25 cm `
or ` l = 75 cm`
If `h` is the height of water filled in the tube , then
` l + h = 120 cm`
` h = 120 - l`
For minimum value of `h , l` is maximum , thus
`h_(min) = 120 - l_(max) = 120 - 75 = 45 cm`
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