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A sonometer wire supports a 4 kg load an...

A sonometer wire supports a 4 kg load and vibrates in fundamental mode with a tunig fork of frequency 416 Hz. The length of the wire between the bridges is now doubled. In order to maintain fundamental mode, the load should be changed to

A

1 kg

B

2 kg

C

4 kg

D

16 kg

Text Solution

Verified by Experts

The correct Answer is:
D
frequency `(f)=(1)/(2l)sqrt((T)/(mu))`
`implies 416=(1)/(2l)sqrt((4g)/(mu))...(i)`
`l.=2l, M.rarr` new load
Fundamental mode is same
`f.=f=416=(1)/(2l.)sqrt((gM.)/(mu))`
`implies416=(1)/(4l)sqrt((M.g)/(mu))...(ii)`
From eq. (i) & (ii) M. = 16 kg.
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