Question

Two waves are traveling in the same direction along a stretched string. The waves are 90° out of phase. Each wave has an amplitude of 4.00cm. Find the amplitude of the resultant wave.

Answer 1

$$y=y_1+y_2=A\cos{(\omega t-kx)}+A\sin{(\omega t-kx)}\\y=\sqrt{2}A\sin{(\omega t-kx+0.25\pi)}$$

The amplitude of the resultant wave:

$$A'=\sqrt{2}A=4\sqrt{2}=5.66\ cm$$