# Phase, Phase Difference and Phase Shift

• unseensoul
In summary, phase refers to the angular argument of a function, while phase difference is the difference in phase between two waves. Phase shift is a shift in the phase of a wave, often occurring in scattering. The constant \phi in a function like sin(2\pi ft + \phi) is usually referred to as the phase, but it can also represent the initial or relative phase. It is an important concept in understanding interference of waves.
unseensoul
What's the difference between Phase, Phase Difference and Phase Shift in terms of waves?

I've taken a look to Wikipedia and a few other sites already, so please do not forward me to them...

"phase" usually refers to the angular argument of a function. E.g.,
$$f(\phi)=\sin(\phi)\;,$$
where $$\phi$$ is the phase. Or, e.g.,
$$f(x,t)=\sin(kx-\omega t)\;.$$
Here, $kx-\omega t$ is the phase. If we have two different waves and the first wave has phase $\phi_1$ and the second wave have phase $\phi_2$ the the "phase difference" is
$$\Delta \phi=\phi_2-\phi_1\;.$$
For example, if I have two wave of the same frequency (2\pi\omega) and wave length (2\pi/k) which travel over different distances (L_1 and L_2, respectively) then there will be a phase difference
$$\Delta \phi=k(L_2-L_1)$$
between the waves.

"Phase Shift" is just what it sounds like--a shift in the phase of a wave. Often this comes up in scattering where the effect of a scatterer on a wave is just to shift the phase of the wave by a "phase shift" (usually denoted by $\delta$). E.g., For scattering a wave of wavelength 2\pi/k off a (very small) hard-sphere of radius R (very small means kR<<1), the scattering phase shift is $\delta=-kR$. This means that if I have a wave which is initially of the form
$$\cos(kz)$$
and I scatter it off a very small sphere, the resultant wave is of the form
$$\cos(kz)-\frac{R}{r}\cos(kr-kR)\;,$$
where R is the (small) size of the sphere and r is the (large) distance to the point of observation (viewing screen or whatever).

Imagining the function sin(2$$\pi$$ft + $$\phi$$) ...

...you're saying that the whole argument (2$$\pi$$ft + $$\phi$$) is what so called "phase"?

So why do people (my lecturers included) keep saying that the phase in the above function is the $$\phi$$?
As you might imagine, this leads me to some confusion...

Sometimes, when people write down a periodic function like $$sin (2\pi f t + \phi)$$, they implicity separate out the time-varying part, which could be the same for different waves, and the constant $$\phi$$ which is allowed to vary. For example, when a light wave passes through a lens, the color of the light stays the same (the $2\pi f t$ part), but the wavefront changes shape (the $\phi$ part).

So, people sometime refer to the absolute phase and relative phase, but all these are just modifiers to 'the phase' of a wave.

Thats initial phase angel , which means now wave has some y (displacement) initally at point x=0 due to the phase angel.
actually phase is important concept when you are dealing with interference of two or more waves . Suppose two waves are having same frequency and same velocity but have to cover diff. distances then at last point they will surely have some diff displacement due to path diff. And if they will have some path diff then there will also be some phase diffrence in btw them which is

§ (phase diff.) = k (wave no.) * (L2-L1)(path diff.)

i hope this help bit!

unseensoul said:
Imagining the function sin(2$$\pi$$ft + $$\phi$$) ...

...you're saying that the whole argument (2$$\pi$$ft + $$\phi$$) is what so called "phase"?

So why do people (my lecturers included) keep saying that the phase in the above function is the $$\phi$$?
As you might imagine, this leads me to some confusion...

technically the phase is the whole argument of the sine function and the phase shift is phi. People seldom get this terminology right though. However, usually the context in which the terminology is used makes it easy to identify the meaning.

Thank you very much for your help. Finally, I got it ;)

## 1. What is phase in science?

Phase in science refers to the stage or state of matter in a substance, typically in relation to its physical properties such as atomic structure and temperature. It can also refer to the stage or state of a process or phenomenon.

## 2. What is phase difference?

Phase difference is a measurement of the difference in the phase of two waves at a specific point in time. It is usually measured in degrees or radians and can be used to describe the relationship between two waves, such as in interference or resonance.

## 3. How is phase difference calculated?

Phase difference is calculated by finding the difference in the phase angles of two waves at a specific point in time. This can be done by measuring the time it takes for two waves to complete one full cycle or by comparing the amplitude and frequency of the waves.

## 4. What is phase shift?

Phase shift refers to the change in the phase of a wave or signal compared to a reference point. It can be caused by factors such as reflections, refraction, or interference and can result in a change in the frequency or amplitude of the wave.

## 5. How does phase relate to wave properties?

Phase is closely related to the properties of a wave such as frequency, amplitude, and wavelength. It can affect the interference and resonance of waves and is an important concept in fields such as optics, acoustics, and electromagnetism.

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