linear density mu of string?

Question

In the arrangement of 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 1.19 m, and the frequency f of the oscillator is fixed at 119 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 286 g or 447 g, but not for any intermediate mass. What is the linear density μ of the string?

How do I reconcile the two masses?

Answer 1

Standing wave will appear at
f=(1/2L)sqrt(T/u)
f- frequency
L- vibrating length of the string
u - linear density = m/L
T- tension

u= T(2fL)^2 since tension T=mg
u= mg(2 f L)^2