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  4. A glass tube of length 1.0 m is completely filled with water. A vibrating tuning fork of frequency 500 Hz is kept over the mouth of the tube and the water is drained out slowly at the bottom of the tube. If velocity of sound in air is 330 ms-1, then the total number of resonances that occur will be

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Q. A glass tube of length $ 1.0\, m $ is completely filled with water. A vibrating tuning fork of frequency $ 500 \,Hz $ is kept over the mouth of the tube and the water is drained out slowly at the bottom of the tube. If velocity of sound in air is $ 330\,m{{s}^{-1}}, $ then the total number of resonances that occur will be

KEAMKEAM 2008Waves

Solution:

$ f=\frac{v}{4l} $ or $ l=\frac{v}{4f} $
$ \therefore $ $ {{l}_{1}}=\frac{v}{4{{f}_{1}}}=\frac{330}{4\times 500}=0.165\,m; $
$ {{l}_{2}}=\frac{3v}{4{{f}_{1}}}=3{{l}_{1}}=0.495; $
$ {{l}_{3}}=\frac{5v}{4{{f}_{1}}}=5{{l}_{1}}=0.825\,m $
And $ {{l}_{4}}=\frac{7v}{4{{f}_{1}}}=7{{l}_{1}}=1.155>1\,m $
Therefore, number of resonance = 3.