A taut rope is given a single displacement amplitude of 2cm at its free end to generate a pulse that travels to the other end. In a second experiment the same amplitude is applied along the rope’s length (push-pull) rather than perpendicular to it. The tension, mass per unit length, and amplitude are identical in both cases. Which assertion about the energy transported to the far end is most accurate?
(a) Approximately the same amount of energy reaches the far end in both cases because the transported energy depends only on A2, not on the disturbance’s direction.
(b) More energy reaches the far end when the disturbance is transverse because bending the rope stores additional elastic energy in the rope segments.
(c) No significant energy reaches the far end in the longitudinal case because compression waves cannot propagate in an ideal rope under tension.
(d) More energy reaches the far end when the disturbance is longitudinal because the particles already move along the rope’s length, so the pulse travels faster and suffers less attenuation.