Two waves, travelling in the same direction through the same region, have equal frequencies, wavelengths and amplitudes. If the amplitude of each wave is 4 mm and the phase difference between the waves is 90°, what is the resultant amplitude?

Sol. Phase difference ∅ = π/2 f and λ are same. So, ω is same. Y base 1 = r sin wt, y base 2 = rsin(wt + π/2) From the principle of superposition y = y base 1 + y base 2 → = r sin wt + r sin (wt + π/2) = r[sin wt + sin(wt + π/2)] = r[2sin{(wt + wt + π /2)/2} cos {(wt – wt – π/2)/2}] ⇒ y = 2r sin (wt + π /4) cos (–π/4) Resultant amplitude = √2 r = 4 √2 mm (because r = 4 mm)