Four harmonic waves of equal frequency and equal intensity I₀ have phase angles 0, π/3, 2π/3 and π. Their resultant intensity is nI₀. Find n.
Physics · Wave Motion
JEE Advanced 2015

Question

Four harmonic waves of equal frequency and equal intensity I₀ have phase angles 0, π/3, 2π/3 and π. Their resultant intensity is nI₀. Find n.

G1 Physics · Accepted Answer

Step 1: Equal intensities mean equal amplitudes. Sum the four unit phasors at phases 0, π/3, 2π/3 and π. Step 2: Their vector sum has magnitude √3 times one amplitude. Intensity scales as amplitude², so resultant intensity = 3I₀. Hence n=3.