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A sonometer wire vibrating in first over...

A sonometer wire vibrating in first overtone has length of `31.25cm`. Tensio in the wire is `256N` and mass per unit length is `10gm//m`. When it is sounded together with a tuning fork `10` beats are heard. If tension in the wire is slightly increased no beats are heard. What is the possible frequency of the tuning fork ?

A

510 Hz

B

505 Hz

C

522 Hz

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Frequency of sonometer wire
`f=(2)/(2xx31.25xx10^(-2))sqrt((256)/(10^(-2)))`
`=(2xx16xx1000)/(2xx31.25)=512Hz`
So possible frequency of tuning fork is `502` and 522 Hz. When frequency of wire is increased by increasing tension beats are not heard.
Which may be due to
`to` both frequency becomes equal
`to` beat frequency is more than the value which can be head
so both answers are possible. Only one is given in options.
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