Question

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 shown in the figure, the fundamental frequency will

• 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 1

The correct option is C become smaller

When a mass of $20kg$ is suspended from the free end of the wire, the tenstion in the string$=20g$.

When tension in the string is as shown in the figure, we consider free body diagram of each block. Let the acceleration of the $14kg$ block be downwards.

Thus $14a=14g-T$

And $6a=T-6g$

$⟹T=8.4g$

Thus tension in the sonometer wire=$2T=16.8g<20g$

Thus the tension in this case is lesser.

Since frequency $\propto \sqrt{T}$, the fundamental frequency becomes smaller.