Two waves represented by $y_1 = 10 \sin 200\pi t$ and $y_2 = 20 \sin \left[ 200\pi t + \frac{\pi}{2}…
Two waves represented by $y_1 = 10 \sin 200\pi t$ and $y_2 = 20 \sin \left[ 200\pi t + \frac{\pi}{2} \right]$ at a point are superimposed at a particular instant. The amplitude of the resultant wave is
(a) $30$
(b) $10\sqrt{5}$
(c) $50$
(d) $10$
Solution
Both waves are $90^\circ$ out of phase.
Hence, $A_R = \sqrt{(10)^2 + (20)^2} = 10\sqrt{5}$
(A vector diagram shows two perpendicular components of lengths 10 and 20 yielding resultant $A_R$.)