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Q.

Two light waves are represented by ${y_1} = a\sin \,\omega \,t\$ and ${y_2} = a\sin \,(\omega \,t + \delta )\$ . When they overlap, the phase angle of the resultant wave is

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a

2 $\delta \$

b

$\delta /3\$

c

$\delta /4\$

d

$\delta /2\$

answer is D.

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Detailed Solution

$Y = a\,\sin \,\omega t + a\sin \,(\omega t + \delta )\$

$= a\,2\,\sin \left( {\frac{{\omega t + \omega t + \delta }}{2}} \right)\cos \left( {\frac{{\omega t - (\omega t + \delta )}}{2}} \right)\$

$= 2a\,\cos \left( {\frac{\delta }{2}} \right)\sin \left( {\omega t + \frac{\delta }{2}} \right)$

Phase angle of resultant wave is $\frac{\delta }{2}\$

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