Question

Two sound waves are given by y=asin(wt-kx) and y = acos(wt-kx). What is the phase difference between two waves?

Answer 1

Answer:

π/4

Explanation:

y1 = a sin(wt-kx) and y2 = acos(wt-kx)

y2 = a sin(wt-kx+π/2)

so, according to the superposition principle,

y = y1+y2

y = a sin(wt-kx)+a sin(wt-kx+π/2)

use Trignometric formula sin a + sin b = 1/2sin((a+b)/2)cos((a-b)/2)

y = a*(2sin*1/2(wt-kx+wt-kx+π/2)cos*1/2(wt-kx-wt+kx-π/2))

y = a *2*sin1/2(2*(wt-kx+π/4)cos(-π/4)

y = a*2*sin(wt-kx+π/4)*1/√2

y = √2a sin(wt-kx+π/4)

so amplitude is √2a and phase difference is π/4.