A frequency generator with fixed frequency of 343 Hz is allowed to vibrate abovea 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) ) .

A frequency generator with fixed frequency of 343 Hz is allowed to vib

1.	A frequency generator with fixed frequency of 343 Hz is allowed to vibrate abovea 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) ) .
Answer» Solution :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`