Halliday, Resnick & Walker — Waves-I: Problem 30

30 In Fig. 16-30, 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 $1.20 \text{ m}$, and the frequency $f$ of the oscillator is fixed at $120 \text{ Hz}$. 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 $286.1 \text{ g}$ or $447.0 \text{ g}$, but not for any intermediate mass. What is the linear density of the string?