A Sonometer wire vibrating in first overtone has length of 31.25 cm . Tension in the wire is 256 N and mass per unig 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?

Options

A. 510 Hz
B. 505 Hz
C. 522 Hz
D. none of these

Answer

C

Explanation

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.