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Two waves represented by y= a sin(wt - kx) and y= a cos(wt - kx) are superposed The resultant wave will have an amplitude?

Two waves represented by y= a sin(wt - kx) and y= a cos(wt - kx) are superposed The resultant wave will have an amplitude?

Grade:12

2 Answers

sanjudev tarikere
33 Points
3 years ago
the 2nd wave can be written as y2=Asin(wt-kx+pi/2)
Now by superposition principle, the resultant wave is y=y1+y2
y=A[sin(wt-kx)+sin(wt-kx+pi/2)]
   =2Acos(pi/4)sin(wt-kx+pi/4)       (Transformation formula used)
This wave equation is telling us that the amplitude of the resultant wave is 2Acos(pi/4) and the the phase angle of the wave is pi/4 , while frequency remaining constant.
 
 
Rishi Sharma
askIITians Faculty 646 Points
one year ago
Dear Student,
Please find below the solution to your problem.

Given, y1 ​= asin(ωt-kx)
y2 ​= acos(ωt-kx)
or y2​ = asin(ωt-kx+2π​)
Phase difference of two waves = 2π​
∵ Resultant amplitude
R = a2 + a2 + 2aacosϕ​
= a2 + a2 + 2a2^cos2π​​
= 2a^2​ (∵cos2π​=0)
R = 2​a.y1
= asin⁡(ωt-kx)

Thanks and Regards

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