Question

A heavy string is tied at one end to a movable support and to a light thread at the other end as shown in figure. The thread goes over a fixed pulley and supports a weight to produce a tension. The lowest frequency with which the heavy string resonates is 120 Hz. If the movable support is pushed to the right by 10 cm so that the joint is placed on the pulley, what will be the minimum frequency at which the heavy string can resonate?

• A. 240 Hz
• B. 120 Hz
• C. 360 Hz
• D. None of these

Answer 1

The correct option is A

240 Hz

Initially,

The point where the strings separate is like a free end for the heavy string and an antinode will form there. So if L is the length of heavy string $L=\frac{\lambda }{4}or\lambda =4L$

On taking the joint to the pulley, the heavy string gets two fixed ends. These both must be nodes

so $L=\frac{\lambda }{2}or{\lambda }^{\prime }=2L$

as we can see that wavelength has become half. Since $f\alpha \frac{1}{\lambda }$ frequency will become double i.e., 240 Hz