In the figure, a string, tied to a sinusoidal oscillator at p and running over a
ID: 1656043 • 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 = 0.9 m, linear density mu = 1.8 g/m, and the oscillator frequency f = 100 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)? (a) Number Units (b) Number UnitExplanation / Answer
a)
m = 4L^2*f^2*u / n^2*g
= (4(0.9)^2*(100)^2*0.00180)/((4)^2*9.8)
= 0.372 kg
b)
m = 2kg
n = sqrt(4*L^2*f^2*u/g)
= sqrt((4*(0.9)^2*(100)^2*0.00180)/9.8)
= 2.44
In order for a standing wave to exist the length of the string must be an integral number of half wavelengths. So the mass cannot setup a standing wave on the string.
So answer is 0.