In the figure, a string, tied to a sinusoidal oscillator at P and running over a
ID: 2102348 • 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 = 0.8 m, linear density ? = 0.8 g/m, and the oscillator frequency f = 160 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 kg (Give 0 if the mass cannot set up a standing wave)?
Explanation / Answer
Part A)
(flambda = sqrt{T/mu})
(160)(.4) = (T/8 X 10^-4)^.5
T = 3.2768 N
T = mg
3.2768 = (m)(9.8)
m = .334 kg (334 g)
Part B)
(160)(x) = [(9.8)/(8 X 10^-4)]^.5
x = .691 m
That value is not an even half factor of .8m (The length of the string) so a 1 kg mass can not set up a standing wave.
Enter the '0' as directed