In the figure below, a string, bed to a sinusoidal oscillator at P and running o
ID: 1609978 • Letter: I
Question
In the figure below, a string, bed 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 1.80 m, and the frequency f of the oscillator Is fixed at 120 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 g or 643.7 g, but not for any intermediate mass. What is the linear density of the string? g/mExplanation / Answer
From the given Figure,
2 lambda = L
lamnda = 1.80/2 = 0.90 m
f = 120 Hz
v = lambda f = 0.90 x 120 = 108 m/s
v = sqrt[ T / linear density]
v^2 = T / mu
v1 / v2 = sqrt(643.7 / 286.1) = 1.50
v = lambda f
lambda1 / lambda2 = 1.50
lambd1 = L = 1.80 m
lambda2 = 1.2 m
v1 = lambda1 f = 216 m/s
v1^2 = T / mu
mu = (643.7 x 10^-3 x 9.8) / (216^2)
mu = 1.352 x 10^-4 kg/m