Phase Relationship

When two waves or more interfere with one other, the notion of phase crucially comes into play. The Greek symbol Phi represents the phase difference. A waveform’s full phase could be described as 2 radians or 360 °. Path difference is intricately related to phase difference as well, in this article we will discuss the phase relationship in depth. 

Before we discuss the phase relationship it is crucial to know about the characteristics and properties of waves.

Wave Characteristics

The primary characteristics of waves:

Wave amplitude – A wave is a kind of energy transportation. The amplitude of the wave is its height, which is commonly measured in metres and is directly proportional to the quantity of energy transported by a waveform.

A wavelength is described as a difference between identical locations in neighbouring cycles of peaks of a wave and is measured in metres.

Period: The duration of a waveform is the amount of time it takes for a component on a medium to finish one full vibrational cycle. Because the interval is a unit of time, it is calculated in seconds/minutes.

Frequency: The quantity of waves crossing a spot in a given amount of time is known as the frequency of a wave. The hertz (Hz) frequency is equal to one wave/second.

Phase

A phase is a fraction of a time frame in which a point finishes upon passing through the zero/reference position concerning the mechanism of vibrations. This notion may also be used for basic harmonic motions in which the phase of oscillating objects and waves is observed. The location of the wave-particle inside a periodic signal is referred to as “Phase” when creating a waveform. The signal’s whole stage is 360 degrees. When two waves or more interfere with one other or pass over the same medium, the notion of phase crucially comes into play. 

Phase Difference

It is a sinusoidal waveform that may be described as “the duration interval through which 1 wave precedes or follows another wave,” thus the phase difference is a comparative attribute of 2 or more waveforms, not just one and is also called “Phase offset” / “Phase angle.”

The Greek symbol Phi represents the phase difference. A waveform’s full phase could be described as 2 radians or 360 °.

A waveform in the leading phase is upfront of some other waveform of the same frequency, whereas a wave in the lagging phase is behind the other wave of the same frequency.

Whenever the phase difference of the two waves is 900 (could be either = + 900 / – 900), the waveforms are also in ‘Phase quadrature.’

Whenever the phase difference of the two waves = 1800 (this can be either + 1800 / – 1800), the waveforms are also in ‘Phase opposition.’

Take a look at the diagram below to get a better understanding of this concept.

Path difference 

If the source of waveforms is initially in phase, they may become in-phase (constructive interference) / out-of-phase (destructive interference) once they reach a remote place due to minor distance variations. Many intriguing phenomena arise as a result of this route difference, including such constructive interference (in the instance of light) and blank spots in lecture halls (in the case of sound). Path differences are responsible for an oil slick and the colours on a soap bubble.

The difference in distance covered by any 2 waves is their path difference. It is the gap between the distance covered by the source and the distance reached by the observer. A path difference is often used to determine whether waves are interfering constructively or destructively.

The phase relationship expressed with an equation

The difference in phase angle between two waves is the definition of phase difference. The Path difference is the difference in the paths taken by the two waves. The phase difference, as well as the path difference, are inextricably linked. They have direct proportionality.

Phase and path difference 

For just any 2 waves with almost the same frequency, phase and path difference are related by ,

Δx= (λ/2π) Δϕ

1. The difference in the path between both the waves is Δx.
2. The difference in phase among 2 waves is ΔΦ

And so phase difference equation becomes, 

   Δϕ=2πΔx/λ 

The unit is radian/degree.

Similarly, the equation of path difference will be:

 Δx = (λ/2π) Δϕ         

The unit is a metre. 

Conclusion

We’ve discussed path difference, phase difference and the relationship between the two.  From the article, it is clear that when two or more waves interact with one another, the concept of phase is vital. It is symbolised by the Greek letter Phi. And The time gap between both the identical points inside the waveform phases of the two sounds represented as a portion of one wave cycle determines the phase difference of those sound waves which are of the same frequency and travelling past a fixed location