Question

On superposition of two waves y=Asin(wt-kx) and y=acos (wt - kx+π/6) . Resultant amplitude is?

Answer 1

Explanation:

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Answer 2

Answer:

A = $\mathsf{A_{o}}$

3rd Option.

Explanation:

Resultant amplitude, A = $\mathsf{2A_{o}cos{\dfrac{{\phi}}{2}}}$

The phase difference between sine and cosine is 90°.

So, $\mathsf{{\phi} = {\dfrac{{\pi}}{2}}+{\dfrac{{\pi}}{6}} = {\dfrac{2{\pi}}{3}}}$

$\mathsf{\dfrac{{\phi}}{2} = {\dfrac{{\pi}} {3}}}$

Now putting in the formula,

A = $\mathsf{2A_{o}cos{\dfrac{{\phi}}{2}}}$

A = $\mathsf{2A_{o}cos{\dfrac{{\pi}}{3}}}$

A = $\mathsf{2A_{o}{\dfrac{1}{2}}}$

A = $\mathsf{A_{o}}$

Hence, 3rd Option is correct one.