What is the Phase Difference Between Waves at Point R?

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Homework Help Overview

The discussion revolves around determining the phase difference between two waves originating from coherent sources P and Q as they meet at point R. The problem involves understanding wave equations and the conditions under which phase differences occur.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the implications of the distances from the sources to point R, questioning whether equal distances lead to a phase difference of zero. Some participants attempt to derive the wave equations for each source and discuss the superposition of the waves.

Discussion Status

The discussion is active, with participants providing mathematical expressions for the wave functions and engaging in clarifying the conditions under which the phase difference can be determined. There is no explicit consensus, as some participants challenge assumptions about the distances from the sources to point R.

Contextual Notes

There is an assumption that the sources are coherent and produce waves of the same phase, but the exact distances PR and QR are not equal, which is a point of contention in the discussion.

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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 ?
 

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


rl.bhat said:
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 ?
 


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.
 


rl.bhat said:
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 !
 

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