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 = (0.10 m)(sin pi x/2)sin 12 pi t, where x = 0 at one end of the rope, x is in meters, and t is in seconds. The length of the rope is?

Question

anonymous · Answer

since it is 2nd harmonic, the length of the rope = the wavelength. The equation for the wave tells us that pi/2 = 2pi/wavelength (the wave number)....
$$kx = 2\pi x/\lambda = \pi x/2$$
then solving for wavelength, we get wavelength = 4 m which is also the length of the rope...

anonymous · Answer

thanks!