What is the Phase Difference Between Waves at Point R?

[thereddevils]

Homework Statement

The diagram attached shows two coherent sources P and Q which produce waves of the same phase with wavelength , labda . If the two waves meet at the point R , the phase difference between waves at R is ??

Homework Equations

y=a sin (omega t + kx)

The Attempt at a Solution

i have problems obtaining the equation for wave p and q respectively , i know i have to find the superposition of the wave ?

 

[rl.bhat]

If P and Q are equidistant from R, then the phase difference between the waves at R is equal to zero.

 

[thereddevils]

If P and Q are equidistant from R, then the phase difference between the waves at R is equal to zero.

but PR is not equal to QR , which part of the question says they are equal ?

 

[rl.bhat]

If PR = x1 and QR = x2, then
y1 = a*sin(ωt + kx1)
Y2 = a*sin(ωt + kx2)
y1 + y2 = a*[sin(ωt+kx1) + sin(ωt+kx2)]
= a*2*sin[ωt + k(x1+x2)/2]*cos[(x1-x2)/2]
= 2*a*cos[(x1-x2)/2]*sin[ωt + k(x1+x2)/2]
Now find the phase difference.

 

[thereddevils]

If PR = x1 and QR = x2, then
y1 = a*sin(ωt + kx1)
Y2 = a*sin(ωt + kx2)
y1 + y2 = a*[sin(ωt+kx1) + sin(ωt+kx2)]
= a*2*sin[ωt + k(x1+x2)/2]*cos[(x1-x2)/2]
= 2*a*cos[(x1-x2)/2]*sin[ωt + k(x1+x2)/2]
Now find the phase difference.

thanks !