Answer to Question #195529 in Mechanics | Relativity for Mohammad Balhas

Question

Two sinusoidal waves travelling in the same direction with the same amplitude, wavelength, and speed, interfere with each other to give the resultant wave: y_res (x,t) = 2 cm sin(4πx-60πt+π/3). The amplitude of the individual waves generating this wave is:

8 cm

2/√3 cm

4/√3 cm

4 cm

2 cm

Answer 1

Gives

$Y=2sin(4\pi x-60\pi t+\frac{\pi}{3})$

Wave is same amplitude speed wavelength

$A'^2=A_1^2+A_2^2+2A_1A_2cos\phi$

$\phi=\frac{\pi}{3}$

Let us Assume same amplitude is $A_1=A_2=$ A

$A'^2=A^2+A^2+2A^2cos(\frac{\pi}{3})$

$2^2=A^2+A^2+2A^2cos(\frac{\pi}{3})$

$4=2A^2+A^2=3A^2$

$3A^2=4$

$A=\sqrt{\frac{4}{3}}$

$A=\frac{2}{\sqrt3}$