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A heavy string is tied at one end to a m...

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 ?
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The correct Answer is:
`240 Hz`.
As end `A` is free so antinode is formed
`:. l = (lambda_(1))/(4)`
Now if support is pushed to right by `10 cm` so that node is formed at joint
`:. L = (lambda)/(2) rArr (lambda_(2) = (lambda_(1))/(2))`
As `V` is same so if wavelength is halfed frequency will be doubled i.e. `240 Hz`
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