Two waves represented by {y₁} = asin frac{{2π}}{λ }left( {vt - x} right) and {y₂}

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14.Waves and Sound

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Two waves represented by ${y_1} = a\sin \frac{{2\pi}}{\lambda }\left( {vt - x} \right)$ and ${y_2} = a\cos \frac{{2\pi }}{\lambda }\left( {vt - x} \right)$ are superposed. The resultant wave has an amplitude equal to

A

Zero

B

$2a$

C

$a$

D

$a\sqrt 2 $

Solution

$\Delta \phi=\frac{\pi}{2} \quad$ so, $\quad \mathrm{A}=\sqrt{\mathrm{a}^{2}+\mathrm{a}^{2}+2 \mathrm{a} \cdot \mathrm{a} \cos 90^{\circ}}$

$\mathrm{A}=\mathrm{a} \sqrt{2}$

Standard 11

Physics

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