In the arrangement in the figure, a string, tied to a sinusoidal oscillator at P

Question

In the arrangement in the figure, a string, tied to a sinusoidal oscillator at P and running over a support at Q, is stretched by a block of mass m. The separation L between P and Q is 1.26 m, and the frequency f of the oscillator is fixed at 116 Hz. The amplitude of the motion at P is small enough for that point to be considered a node. A node also exists at Q. A standing wave appears when the mass of the hanging block is 208 g or 325 g, but not for any intermediate mass. What is the linear density mu of the string?

Explanation / Answer

here tension T = mg = 0.208*9.8 = 2.0384 N

f = 4v/2L

v = f*L/2 = (116*1.26)/2 = 73.08 m/s

but v = sqrt(T/u)

u = T/v^2 = 2.0384/(73.08*73.08)

linear density = u = 3.82*10^-4 kg /m^2

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