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

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by ashikikbal01

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by ashikikbal01

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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**

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)

⇒