Question

when the waves y1=A sin Wt and y2=A cos Wt are superposed, then resultant amplitude will be??????

Answer 1

y₁ = A sin wt
y₂ = A cos wt

After superposition, the wave is given by
y = y₁ + y₂
⇒ y = A sin wt + A cos wt
⇒ y = A [ sin wt + cos wt]
⇒ y = A [ sin wt + sin (90-wt)]
⇒ y = A [ 2 × sin(wt+90-wt)/2 × cos (wt-90+wt)/2]
⇒ y = A [ 2 × sin 45 × cos (wt-45)]
⇒ y = A [ 2/√2 × cos (90-wt)]
⇒ y = √2 A cos(90-wt)
⇒ y = √2 A sin wt