Phase Difference and Path Difference

Before we discuss the phase difference and path difference of a wave and the relationship between these two numbers, we need first to know what type of waves and their attributes.

Waves of Different Kinds

The following are the two fundamental types of waves:

1. Mechanical Waves: These oscillations of matter may be characterized as waves. To transport energy, these waves require a medium. Sound waves, water waves, rope waves, and so on are all examples of mechanical waves.

2. Electromagnetic Waves: All of those are vibrations that do not demand any medium to move and distribute their energy. This implies that they may move in a vacuum like x-rays, gamma rays, and UV rays.

Wave Properties

Wavelength: The separation between the two successive crests or troughs of a pulse is called its wavelength, measured in meters.

Displacement: Displacement is a particle’s total distance from its mean location, always measured in meters.

Amplitude: Amplitude seems to be the elevation of a wavelength’s crest or depth of a wavelength’s trough, or it may be characterized as the greatest movement. Amplitude, like displacement, is measured in meters as well.

Time Period: The time required for a wave to complete one entire oscillation is known as its period. The unit of measurement for a wave’s time span is the second.

Time period = 1/frequency

Frequency: The wave’s frequency is calculated as the number of entire vibrations made by such a wave in one second, and the frequency unit is Hertz (Hz).

frequency = 1/time period

These were some frequent wave qualities; now, we will discuss two more wave properties: phase differences and path differences. These two wave qualities are addressed more below.

Phase Difference

Waves cause particles to oscillate. When particles travel back and forth, they go through phases ranging from 0° to 360°. Where 1800 denotes one period. The particles move through phases in which the particle travels one wavelength. In one period of time, a molecule traverses the range of one wavelength. When particles move in such a method that their displacement equals their wavelength, they traverse through phases ranging from 0 to 3600.

The phase difference is the disparity in the phases of two particles at any two moments where their location and motion are the same.

The temporal period by which one wave leads or lags another is defined as the phase difference of a sine wave. It is important to emphasize that phase difference is a relative attribute of two or more waves, not just one.

The phase discrepancy is the “Phase offset” or “Phase angle.” The phase difference is represented by the Greek letter Phi, which is represented as to ɸ.

Path Difference

The route difference between any two waveforms is the distance they traverse. It is the difference in distance between the source and the observer. The path difference is often used to determine both constructive and destructive wave interference.

Relation between Phase Difference and Path Difference

For any two waves of the same frequency, the phase difference and path difference are connected as-.

Phase Difference = (2π * path difference)/wavelength

The SI unit of path difference and phase difference is one since neither has a SI unit. The path difference is the cumulative number of waves in a phase, whereas the phase difference is given in terms of radians between any two successive places.

Difference between Path and Phase Difference

Path difference is the variation in the paths taken by the two waves, expressed in terms of the wavelength of the associated wave. It is directly related to phase difference. The nature of the interference pattern is determined by phase difference, whereas route difference determines phase difference. Quantum mechanics is connected to phase difference. If the path difference between two waves is an integral multiple of the wavelength, the requirement for constructive interference is met. In contrast, if the path difference between two waves is an odd multiple of half wavelength, the requirement for destructive interference is satisfied.

While phase difference is the disparity between two wave’s reference points, it is the amount by which one wave differs from the other. For example, if one wave has zero displacement at the origin and the other has some displacement, there is a change, which would be their phase difference. For example, the sine wave is nil at the center, but the cos wave is 0 at pi/2. As a result, the phase difference is pi/2. In actuality, the cos wave is simply a sine wave that has been phase-shifted.

Conclusion

The difference in phase angles between two waves is called phase difference. Path difference, from the other extreme, is defined as the difference between two wave’s paths. I hope you got the relationship and conversion between the wave’s Phase Difference and Path Difference.