A rope, under a tension of 200 N and fixed at both ends, oscillates in a second-harmonic standing wave pattern. The displacement of the rope is given by : y=0.1sin(πx2)sin12πt.
Where x = 0 at one end of the rope, x is in meters and t is in seconds. What is the mass of the rope?
Since the rope oscillates in second harmonic, the length of the rope is equal to the wavelength.
Thus L=λ=2ππ/2=4m
Speed of the wave is given by-
√Tμ=ωk
⟹√200m/4=12ππ/2
⟹m=2518kg