The displacement equations of two interfering waves are y₁ = 10 sin(ωt + π/3) cm and y₂ = 5[sin(ωt) + √3 cos(ωt)] cm. The amplitude of the resultant wave is ______ cm.
Physics · Circular Motion
JEE Mains 31 January 2023 Shift 2 Evening Shift

Question

The displacement equations of two interfering waves are y₁ = 10 sin(ωt + π/3) cm and y₂ = 5[sin(ωt) + √3 cos(ωt)] cm. The amplitude of the resultant wave is ______ cm.

G1 Physics · Accepted Answer

Expand y₁: 10[sinωt cos60° + cosωt sin60°] = 5sinωt + 5√3cosωt. This is exactly equal to y₂. Hence the two waves are in phase and each has amplitude 10 cm. Resultant amplitude = 20 cm.