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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

`502 Hz`

B

`510 Hz`

C

`505 Hz`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
A sonometer ………….
Frequency of sonometer wire `f = (2)/(2xx31.25xx10^(-2)) sqrt((256)/(10^(-2)))`
`= (2xx16xx1000)/(2xx31.25) = 512 Hz`
So possible frequency of tuning for `k` is 502 and `522 Hz`. When frequency of wire is increased by increasing tension, betats are not heard. Whcih may be due to
`rarr` Both frequency becomes equal `(f = 522 Hz)`
`rarr` Beat frequency is more than the value which can be heard (16 beats) `(f = 502 Hz)` . So both answers are possible. Only one is given in options.
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