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A frequency generator with fixed frequen...

A frequency generator with fixed frequency of 343 Hz is allowed to vibrate above a 1.0 m high tube . A pump is switched on to fill the water slowly in the tube . In order to get resonance , what must be the minimum height of the water ? (Speed of sound in air is `343 ms^(-1)` ) .

Text Solution

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The wavelength , `lambda = (c)/(f) implies lambda = (343 ms^(-1))/( 343 Hz) = 1.0` m
Let the length of the resonant columns be `L_1 , L_2` and `L_3` . The first resonance occurs at length `L_1`
`L_(1) = (lambda)/(4) = (1)/(4) = 0.25` m
The second resonance occurs at length `L_(2) = (3lambda)/(4) = (3)/(4) = 0.75` m
The third resonance occurs at length `L_(3) = (5 lambda)/(4) = (5)/(4) = 1.25` m
Since total length of the tube is 1.0 m the third and other higher resonances do not occur . Therefore , the minimum height of weight `H_("min")` for resonance is ,
`H_("min") = 1.0 m - 0.75 = 0.25 m`
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