Halliday, Resnick & Walker — Waves-I: Problem 28

28 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 $m$. Separation $L = 1.20 \text{ m}$, linear density $\mu = 1.20 \text{ g/m}$, and the oscillator frequency $f = 120 \text{ Hz}$. 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) What mass $m$ allows the oscillator to set up the fourth harmonic on the string? (b) What standing wave mode, if any, can be set up if $m = 1.00 \text{ kg}$?