Calculate Phase Relationship

Phase relationships state the relation between different characteristics of a longitudinal wave, such as phase difference, path difference, the wavelength of the wave, amplitude of the wave, frequency of the wave, etc. The location and timing of a spot inside a wave cycle of a repeated waveform are defined by phase. Phase is the inherent quality of physical waves.

The phase difference across sound waves, rather than the absolute phases of the signals, is usually what matters. When two sound waves are combined, for example, the phase difference in the two waves is crucial in defining the waveform that results. This article will explain what a phase angle is, phases in waves and the phase difference formula. 

What Is Phase In Waves?

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 time difference between the same points inside the wave cycles of the two frequencies is expressed in the form of a fraction for a single wave cycle that determines the phase difference traveling past a fixed location between two sound waves.

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.

Characteristics Of Wave

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.

Wavelength – A wavelength is described as a difference between identical locations in

neighbouring cycles of peaks of a wave and are measured in metres.

Time Period – The duration of a waveform is the amount of time it takes for a

component on a medium to finish one complete 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 Difference Formula

It is a sinusoidal waveform that may be described as “the duration interval through which one 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 phase difference between two sound waves having the same frequency that are precisely aligned is zero and they are in phase. Two in-phase waves combine to form a sound wave with an amplitude equal to the sum of the two waves’ amplitudes. This is referred to as “constructive interference.”

The sound waves are said to be “not in phase” if one of the two sound waves of the same frequency is moved by a one-half cycle relative to the other so that one wave is at its most significant amplitude while the other is at its minimum amplitude. 

When two out-of-phase waves are combined, they cancel each other out exactly. This approach is known as “destructive interference,” used in noise-cancelling headphones. Both constructive and destructive interference explains many valuable features of the ocean.

Path Difference In Sound Waves

Suppose 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 due to this route difference, including 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 two 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. 

Path And Path Difference Formula

The difference in phase angle between the two waves is the definition of phase difference. The Path difference is the actual 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. For just any two waves with almost the same frequency, phase and path, the 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 two waves is ΔΦ and so the 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. You read about the phase difference formula, phases in waves, and phase angle from the article. It is clear that when two or more waves interact, the concept of phase is vital. It is symbolised by the Greek letter (ɸ)Phi and the time gap between 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 of the same frequency and travelling past a fixed location.