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sinusoidal oscillator?
A string, tied 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 1.30 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 447.0 g, but not for any intermediate mass.
What is the linear density of the string?
MORE: OSCILATOR-----POINT P --------------------POINT Q
Extending down from Q is the hanging BLOCK also assume n=4
1 Answer
- kirchweyLv 71 decade agoFavorite Answer
Frequency ratio = sqrt(T1/T2) = 0.8, a lowest-integer ratio of 4:5. Then when T = g*0.2861 N, the fundamental frequency f0 = 120/5 = 24 Hz, and when T = g*0.447 N, f0 = 120/4 = 30 Hz.
From the ref., you can derive linear density m/L = T/(4*f0^2*L^2)
m/L = 7.20E-4 kg/m.
