A heavy string is tied at one end to a movable support and to a l… - Vidyadip

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 120Hz. If the movable support is pushed to the right by 10cm so that the joint is placed on the pulley, what will be the minimum frequency at which the heavy string can resonate?

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Answer

Initially because the end A is free, an antinode will be formed.
So, $\text{l}=\frac{\text{Ql}_1}{4}$
Again, if the movable support is pushed to right by 10m, so that the joint is placed on the pulley, a node will be formed there.
So, $\text{l}=\frac{\lambda_2}{2}$
Since, the tension remains same in both the cases, velocity remains same.
As the wavelength is reduced by half, the frequency will become twice as that of 120Hz i.e. 240Hz.

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