Two harmonic waves are represented in SI units by, y1 (x, t) = 0.2 sin (x − 3.0t) and y2 (x, t) = 0.2 sin (x−3.0t + ϕ). What is the expression for the sum y = y1 + y2 for ϕ =π2.
y = 0.28 sin (x - 3.0t+π4)
The two waves y1(x1t)=0.2sin(x−3.0t)
y2(x1t)=0.2sin(x−3.0t+ϕ)
Given,ϕ=π2
Drawing a phase diagram
Resultant amplitude A=√(0.2)2+(0.2)2+2×0.2×0.2cos(π2)
A=√2×0.2=0.28 m
The new phase θ=tan−1(0.20.2)=π4
Sot the wave equation for y=y1+y2
y=0.28sin(x−3.0t+π4)