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 (15-E12). 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 1.20 Hz. If the movable suppor 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 ?

Answer 1

Initially because the end 'A' is free, an antinode will be formed.

So, $I=\frac{{\lambda }_1}{4}$

Again if the movable support is pushed to right by 10 m, so that the joint is placed on the pulleys, node will be formed there

So, $I=\frac{\lambda g}{2}$

Since the tension remains same in both the case, velocity remains same as the wave length is reduced by half, the frequency will become twice as that of 120 Hz i.e. 240 Hz.