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Two tuning forks A and B give 9beats in ...

Two tuning forks A and B give 9beats in 3 seconds. A resounds with a closed column of air 15cm long and B with an open column 30.5 cm long. Calculate their frequencies (neglect end correction).

Text Solution

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For closed column,
`l=15cm=0.15m`
For open column, `l=30.5cm =0.305m`
Let `v_(1)v_(2)`, be the frequencies of the tuning forks A and B respectively.
As, tuning fork A resounds with a closed column
`:. v_(2)=(upsilon)/(4l) =(upsilon)/(4xx0.15)=(upsilon)/(0.60)` ...(i)
The fork B resounds with an open air column
`:. v_(2)=(upsilon)/(2l)=(upsilon)/(4xx0.305)=(upsilon)/(0.61)` ...(ii)
As, forks A and B produced` 9//3 =3` beats per second, therefore, `v_(1)-v_(2)=3`
or `(upsilon)/(0.60)-(upsilon)/(0.61)=3`
or `v(0.61-0.60)=3xx0.60xx0.61`
or `upsilon=(3xx0.60xx0.61)/(0.01)=109.8ms^(-1)`
`v_(1)=(upsilon)/(0.60)=(109.8)/(0.60)=183Hz`
and `v_(2)=(upsilon)/(0.61)=(109.8)/(0.61)=180Hz`
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