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  • A tuning fork of frequency 340 Hz resonates in the mth mode with an air column of length 125 cm in a cylindrical tube closed at one end. When water is slowly poured into it, the min

A tuning fork of frequency 340 Hz resonates in the mth mode with an air column of length 125 cm in a cylindrical tube closed at one end. When water is slowly poured into it, the minimum height of water required for observing resonance once again is ________cm.

(Velocity of sound in air is \mathrm{340 \mathrm{~ms}^{-1}})

Option: 1

50


Option: 2

100


Option: 3

200


Option: 4

300


Answers (1)

best_answer

For resonance to occur

f=(2n-1)\frac{V}{4l}

for f=340 Hz \ and \ V=340 \ m/s

l=\frac{2n-1}{4}

So Height of water required =  h=1.25-l

For n=0

l=0.25 m \ \ and \ h=1 m 

For n=1

l=0.75 m \ \ and \ h=0.5 m 

For n=2

l=1.25 m \ \ and \ h=0 m

h=0 means no water is there in the tube (which is already given in the question)

So the minimum value of h will be 0.5 m (i.e for n=2 case)

(see the below figure for n=0, n=1 and n=2 for better understanding )

 

 

 

Posted by

Rakesh

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