Question

A graph with vertical axis Energy Unit and horizontal axis Amplitude Unit. A line goes in straight segments from 1 16 to 2 9 to 4 1.
Tara prepared a report to show how the amplitude of waves affects the energy of waves. Is her graphical representation correct? Why or why not?

Answer 1

No — Tara’s graph is not correct.

Reason:
- For waves the energy E is proportional to the square of the amplitude A: E ∝ A^2 (so E = kA^2 for some constant k). That means energy increases with amplitude and the graph of E vs A is a parabola (not straight-line segments).
- Tara’s points (A,E) = (1,16), (2,9), (4,1) show energy decreasing as amplitude increases and she connected them with straight lines, implying a piecewise-linear relation. That contradicts the physical law E ∝ A^2 and is internally inconsistent: if E = kA^2 and k = 16 from the first point, then E(2) would be 16·2^2 = 64 and E(4) = 16·4^2 = 256, not 9 and 1.

Therefore the plotted points and the linear connections are incorrect for the amplitude–energy relationship; the correct plot should be a smooth upward-opening parabola (E = kA^2).