In a sonometer wire, the tension is maintained by suspending a `20kg` mass from the free end of the wire. The fundamental frequency of vibration is `300Hz`.

If the tension is provided by two masses of `6kg` and `14kg` suspended from a pulley as show in the figure the fundamental frequency will

Options

A. still remain `300Hz`
B. become larger
C. become smaller
D. decrease in the present situation and increase if the suspended masses of `6kg` and `14kg` are interchanged

Answer

C

Explanation

Let a be the acceleration in the cord.
Then `T-6g=6a`
`14g-T=14a`
Adding both, `8g=20aimpliesa=(8g)/(20)`
`:.T=(6xx8g)/(20)+6g=6g((8)/(20)+1)`
The total effective tension in the sonometer wire `T.=2T`
When in the first case the tension was `20g`. Hence, the effective tension is reduced.
Since `f=(1)/(2L)sqrt((T.)/(m))`