A pulse is created by flicking the free end of a long, uniform rope that is under constant tension. In a separate trial, the same rope is flicked in exactly the same manner except that the hand moves twice as far from the equilibrium position before releasing the rope.
Assume the rope properties and the flicking time interval are identical in the two trials.
(a) Define the amplitude of a mechanical wave pulse and identify the physical feature of the rope that corresponds to the amplitude in this experiment.
(b) Using qualitative reasoning, compare the amount of energy transported along the rope by the larger-amplitude pulse with the energy transported by the smaller-amplitude pulse. State the factor by which the energy changes and justify your answer.
(c) Does the speed of either pulse differ from the other once they are well clear of the hand? Explain your reasoning in terms of relevant physical quantities for a wave on a stretched rope.
(d) If the same two flicking motions were applied to a loudspeaker cone instead of a rope, describe how the perceived loudness of the resulting sounds would compare. Justify your answer based on the physical interpretation of amplitude for sound waves.