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Questions  

Two waves 
      y1=A1sin(ωtβ1),  y2=A2sin(ωtβ2)
Superimpose to form a resultant wave whose amplitude is

a
A12+A22+2A1A2cos(β1−β2)
b
A12+A22+2A1A2sin(β1−β2)
c
A1+A2
d
|A1+A2|

detailed solution

Correct option is A

Phase difference between the two waves is   φ=(ωt−β2)=(ωt−β1)=(β1−β2)∴Resultant amplitude A=A12+A22+2A1A2cos(β1−β2)

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