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If the tension and diameter of a sonomet...

If the tension and diameter of a sonometer wire of fundamental frequency n is doubled and density is halved, then its fundamental frequency will become .......... .

A

`(n)/(4)`

B

`sqrt(2)n`

C

n

D

`(n)/(sqrt(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
`n=(1)/(2l)sqrt((T)/(pir^(2)P))`
`P_(1)^(.)=(P)/(2)` , `T^(.)=2T` and `D^(.)=2D` (or)`r^(.)=2r`
`n^(.)=(1)/(2l)sqrt((2T)/(pi(2r)^(2)(P)/(2)))=(1)/(2l)sqrt((T)/(pir^(2)l))=n`
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