Physics Question on Transverse Waves

Question

The equations of two waves are given by :
y1 = 5 sin 2π(x – vt) cm
y2 = 3 sin 2π(x – vt + 1.5) cm
These waves are simultaneously passing through a string. The amplitude of the resulting wave is :

Answer 1

Solution

y 1 = 5sin(2π x – 2π vt)
y 2 = 3sin(2π x – 2π vt + 3π)
⇒ Phase difference = 3π
⇒ Anet= $\sqrt{A_1^2+A_2^2+2A_1A_2cos(3\pi)}$
⇒ Anet=2 cm
The correct option is (A): 2 cm