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Q.

Three harmonic waves having equal frequency v and same intensity I0 , have phase angles  0,π4 and  −π4 respectively. When they are superimposed the intensity of the resultant wave is close to:

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a

0.2  I0

b

3  I0

c

5.8  I0

d

I0

answer is C.

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Detailed Solution

A→1=Acos⁡π4i^+Asin⁡π4j^A→2=Ai^A→3=Acos⁡π4i^−Asin⁡π4j^∴A→net =(1+2)Ai^Anet =(1+2)A We know that, Intensity ∝( Amplitude )2⇒Inet =KAnet 2=(1+2)2A02KBut,I0=KA02∴Inet =(1+2)2I0=5.8I0
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