In Fig. below, a string, tied to a sinusoidal oscillator at P and running over a
ID: 1728865 • Letter: I
Question
In Fig. below, a string, tied to a sinusoidal oscillator atP and running over a support at Q, is stretchedby a block of mass m.The separation L betweenP and Q is 2.00 m, and the frequency fof the oscillator is fixed at 127 Hz. The amplitude of the motionat P is small enough for that point to be considered anode. A node also exists at Q. A standing wave appearswhen the mass of the hanging block is 3503.5 g or 2574.0 g, but notfor any intermediate mass. What is the linear density (in g/m) ofthe string?
Explanation / Answer
L = 2.00 m, f = 127 Hz, m1 = 3.5035 kg, m2 =2.5740 kg, find linear density L = (/2)*k where k in an integer. so = 2L/k speed of wave v = f = 2fL/k v = (mg/) = 2fL/k so m * k = constant m1 k1 = m2k2 k2/k1 = (m1/m2)= 1.16666 = 7/6 so k1 = 6 (m1g/) = 2fL/k1 =m1gk12/(2fL)2 =4.79*10-3 kg/m = 4.79 g/m