Physics · Waves · NEET
No, but they are linked. Path difference is a distance in metres between two points. Phase difference is an angle in radians. The bridge formula is: phase difference = (2*pi / lambda) * path difference. So one full wavelength of path (lambda) equals a phase difference of 2*pi radians. This link is used a lot in interference and NEET numericals.
Phase sits inside sin() or cos(), and those functions only take angles. In y = a sin(kx - wt), the term (kx - wt) must come out as an angle, so its unit is radian. Distance (x) is turned into an angle by multiplying with k, because k has units rad/m. So k*x gives radians, never metres.
phi is the initial phase or phase constant. It fixes where the particle starts at x = 0 and t = 0. If phi = 0, the particle starts at zero displacement moving up. A non-zero phi just shifts the whole wave sideways in time. It does not change amplitude, wavelength or frequency.
Two points are in phase when their phase difference is 0, 2*pi, 4*pi... (any whole number times 2*pi). They move together, up and down at the same time. They are out of phase (exactly opposite) when the phase difference is pi, 3*pi, 5*pi... Points one wavelength apart are in phase; points half a wavelength apart are out of phase.
Freeze time (t is fixed), so the phase at any point is (kx - wt + phi). The phase difference between point 2 and point 1 is k*(x2 - x1) = k * (path difference). Since k = 2*pi/lambda, this equals (2*pi/lambda) times the distance between them. Time cancels out because both points are looked at the same instant.
For a travelling harmonic wave y(x, t) = 2.0 cos[2*pi(10t - 0.0080x + 0.35)], where x and y are in cm and t in s, the phase difference between the oscillatory motion of two points separated by 0.5 m is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
For a wave y = a sin(kx - wt + phi), the phase is the whole bracket: phase = (kx - wt + phi). It is an angle in radians that gives the particle's exact stage in its cycle.
Phase difference = (2*pi/lambda) * (path difference), or equally k * (path difference), where k = 2*pi/lambda. Both distances must be in the same unit.
One wavelength of separation gives a phase difference of 2*pi radians (360 degrees), so the two points are in phase and move exactly together.
A crest and the neighbouring trough are half a wavelength apart, so the phase difference is pi radians (180 degrees). They are exactly out of phase.
For two fixed points looked at the same instant, the time term cancels, so the spatial phase difference k*(delta x) stays constant. This is why we can talk about a fixed phase difference between two positions.
