In the figure, a string, tied to a sinusoidal oscillator at P and running over a
ID: 1783565 • Letter: I
Question
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. Separation L 1.4 m, linear density = 0.9 g/m, and the oscillator frequency f= 130 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-2 kg (Give 0 if the mass cannot set up a standing wave)? Oscillator PExplanation / Answer
frequency f = 130 Hz
L =1.4 m
Linear density = 0.9g/m = 0.9*10^-3 Kg/m
(a)
n = 4
Mass m = (4 L^2 f^2 )/n^2 g ---------------- (1)
=0.760
(b)
Put m = 2 Kg in equation(1) then
n = 6.08
But n must be an integer, so n = 6.08 is impossible.
Thus with m = 2 Kg, the oscillator can't form standing waves.
So mode = 0