Progressive waves: phase and path difference
Read stated displacement-distance and displacement-time data, calculate phase differences on a periodic progressive wave, and relate path difference to arrival phase for initially in-phase waves of common frequency and wavelength with no additional phase shifts.
What a learner can do afterwards
- Reads amplitude, wavelength and period from explicitly stated displacement-distance and displacement-time data and identifies the axes
- States the phase difference between two points a stated fraction of a wavelength apart
- Turns a path difference into a phase difference and says whether the two waves arrive in phase
1 · Read
A displacement-distance graph records positions at one instant. Wavelength is the distance between neighbouring matching points. You can also calculate it from stated graph data: crests at 0 m, 4 m and 8 m give wavelength 4 m. Subtract neighbouring positions, not displacement values. The data here describe a graph; they are not a drawn wave curve.
Displacement is measured from rest, so rest has displacement zero. Its sign gives direction; its magnitude is the distance from zero. Amplitude is the greatest displacement magnitude on either graph. Values from +4 cm to −4 cm give amplitude 4 cm, not 8 cm. In an ideal mechanical progressive-wave model, the disturbance transports energy while material oscillates about rest without net transport with the pattern.
For two points on one periodic progressive wave at the same instant, separation ÷ wavelength counts cycles. Multiply by 360 for the positive accumulated phase gap in degrees. For residual phase, subtract whole cycles: 2.2 − 2 = 0.2 cycles. Whole-wavelength gaps give the same phase; a nonzero remainder gives different phases. Antiphase is a half-cycle difference, not cancellation between separated points.
Path difference is the difference between two routes to a meeting point. Assume initially in-phase sources, common frequency and wavelength, and no extra phase shifts along the routes. Then path difference ÷ wavelength × 360 gives the arrival phase gap. A half-wavelength path difference gives antiphase arrival. This alone does not promise complete cancellation.
Initially in-phase sources with common frequency and wavelength and no extra phase shifts arrive in phase for whole-number wavelength path differences: crests occur together. Sinusoidal waves rise and fall smoothly like a sine curve, with regularly spaced crests and troughs. For sinusoidal waves of common frequency along the same line, equal amplitudes in antiphase cancel completely where they overlap. Unequal amplitudes generally leave a nonzero result.
Use the axes and stated data to find amplitude, wavelength or period. Convert a separation to phase. Path difference alone gives arrival phase only under the stated source and path assumptions.
Original lesson and practice questions written for this learning dataset.
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