Grade 12Wave Optics

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

Anshuman Mishra

8 Years agoGrade 12

2 Answers

sanjudev tarikere

8 Years ago

the 2^nd 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

6 Years 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 = 2a.y1
= asin⁡(ωt-kx)

Thanks and Regards