A shallow ripple tank is used to study water waves generated by an oscillating paddle. The paddle produces periodic waves of fixed frequency f in water of uniform depth. A photodiode array measures the energy transported by the wave across a line segment of length L in the tank. When the paddle operates with peak vertical displacement (amplitude) A0, the total energy E0 crossing the line segment during one period is recorded.
Afterward, the experiment is repeated with the paddle displacement increased to 1.8A0 while all other conditions (including frequency) remain unchanged.
(a) Derive an expression for the ratio E0E1 of the energy transported during one period at the larger amplitude (E1) to the energy transported at the original amplitude (E0). Clearly state any proportional relationships you use.
(b) The experimental result yields E1=3.3E0. Compare this measured ratio with the expression you obtained in part (a) and discuss two plausible sources of discrepancy between the theoretical prediction and the measured value.
(c) Describe a modification to the experimental setup that would allow the investigation of whether wave speed depends on amplitude in this system. Outline the measurements you would take and the criteria you would use to draw a conclusion.