Physics

Physics

Problem

A water-surface wave of amplitude A0A_0 carries an intensity I0I_0 toward a boundary where 80%80\% of the wave’s energy is transmitted and 20%20\% is reflected. The intensity of a wave is proportional to the square of its amplitude. Which relationship between the transmitted amplitude ATA_T and the reflected amplitude ARA_R is most consistent with the information? a) AT≈4ARA_T \approx 4A_R b) AR≈2ATA_R \approx 2A_T c) AT≈2ARA_T \approx 2A_R d) AT≈2 ARA_T \approx \sqrt{2}\,A_R
Intuitive explanation

Wave intensity depends on amplitude squared, so you need to connect energy fractions to amplitude ratios. Since 80% of energy transmits and 20% reflects, the transmitted and reflected waves each carry those fractions of the original intensity—and intensity scales as A2A^2. Find what amplitudes would produce intensities in an 80:20 ratio, then express that relationship.

Intuitive explanation

Wave intensity depends on amplitude squared, so you need to connect energy fractions to amplitude ratios. Since 80% of energy transmits and 20% reflects, the transmitted and reflected waves each carry those fractions of the original intensity—and intensity scales as A2A^2. Find what amplitudes would produce intensities in an 80:20 ratio, then express that relationship.

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