Question

two waves represented by y= a sin(wt - kx) and y= a cos(wt - kx) are superposed The resultant wave will have an amplitude
a) a
b)√2a
c) 2a
d) 0

Answer 1

according to my opinion it is (b)

Equation for the waves are,

Y1=A sin (ωt−kx) and Y2=A cos (ωt−kx)=A sin (ωt−kx+π2)

So, according to the superposition principle, the resultant wave equation is,

Y=Y1+Y2=A sin (ωt−kx) +A sin (ωt−kx+π2)⇒ Y=A{sin (ωt−kx)+sin (ωt−kx) cos (π2) + cos (ωt−kx) sin (π2)}⇒ Y=2A cos (π2/2) sin (ωt−kx+π2/2)⇒ Y=2√A sin (ωt−kx+π4)

Therefore, the amplitude of the resultant wave is 2√A.