Phase difference between waves

• thereddevils
In summary, the diagram shows two coherent sources P and Q that produce waves of the same phase with wavelength lambda. When these waves meet at point R, the phase difference between them is dependent on their distance from R. If P and Q are equidistant from R, the phase difference is zero, but if they are not equidistant, the phase difference can be found using the equations y1 and y2.
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 ?

Attachments

• waves.bmp
216.7 KB · Views: 568

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 !

1. What is the definition of phase difference between waves?

The phase difference between waves is a measure of the difference in their positions in their respective cycles. It is the amount by which one wave lags or leads the other in terms of their peaks or troughs.

2. How is phase difference calculated?

Phase difference can be calculated by finding the time difference between corresponding points on two waves, and then converting that time difference into a fraction of a full cycle. This fraction represents the phase difference between the two waves.

3. Why is phase difference important in the study of waves?

Phase difference is important because it can affect the interference and superposition of waves. When two waves with the same frequency and amplitude have a phase difference of 180 degrees, they will cancel each other out, resulting in destructive interference. On the other hand, a phase difference of 0 degrees will result in constructive interference.

4. Can phase difference be negative?

Yes, phase difference can be negative. This occurs when one wave is ahead of the other by more than half a cycle. In this case, the phase difference is represented as a negative fraction of a full cycle.

5. How does frequency affect phase difference?

The frequency of a wave does not directly affect its phase difference. However, when comparing two waves with different frequencies, the phase difference will change at a different rate. This is because a higher frequency wave completes more cycles in the same amount of time compared to a lower frequency wave.

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