A 12m-long rope of linear mass density μ=0.015kgm−1 is kept under a constant tension of 30N. A mechanical driver attached to the left end can oscillate the rope either side-to-side (horizontal) or along the length of the rope (in-and-out). For each driving mode the amplitude of oscillation is 0.080m and the frequency is 2.5Hz. When the driver operates in the in-and-out mode, the resulting longitudinal disturbance on the rope is observed experimentally to travel at 200ms−1. Answer the following.
(a) Calculate the speed of the side-to-side disturbance that travels along the rope.
(b) Using your result from part (a), determine the wavelength of the side-to-side disturbance.
(c) Qualitatively compare the rates at which energy is transported by the two disturbances over the first meter of the rope, given that the driver supplies the same peak force in both modes. Clearly state which disturbance is expected to transmit more energy and why.
(d) Explain how the two modes of oscillation lead to different orientations of particle displacement relative to the rope’s length, and identify which mode produces a transverse wave and which produces a longitudinal wave.