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  1. Can please someone give a simple explanation of the phase of a waveform, particularly the sine function?

  2. Also, what is the angular frequency, and how does it differ from the frequency?

sammy gerbil
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user501436
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    All of these terms have nice Wikipedia entries. Is there something specific you find confusing about the explanations found there? – user143410 Nov 15 '17 at 14:52
  • Have a look at these two answers for phase and phase difference. https://physics.stackexchange.com/questions/310851/leading-lagging-terminology-for-sinusoidal-waves/310890#310890 and https://physics.stackexchange.com/questions/232641/what-is-the-definition-of-phase-lag-and-phase-difference/232647#232647 – Farcher Nov 15 '17 at 15:04
  • @user143410 I searched on Wikipedia for their definitions but the problem is that I am still a high school student and I don't understand everything wirtten there. – user501436 Nov 15 '17 at 15:15
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    I'm simply suggesting you specify which parts weren't clear to you. In general, targeted questions which address your specific confusion are superior to asking for a general introduction. As your question is written, anything one might reply with is surely expressed in some form on those Wikipedia pages. It's difficult to anticipate which parts are confusing to you without more info. – user143410 Nov 15 '17 at 15:26
  • Okay. Actually, we learned today that in undamped free oscillations of a horizontal elastic pendulum, at any instant t we can say x=Xm sin(omega zero t + phi) where omega zero t + phi is the phase expressed in radians. I asked my teacher what do you mean by phase and what practically is it? Why is it expressed in radians while we have nothing related to angles in the whole pendulum? He told me that the phase is not an angle but a "state" but I still didn't understand and I got more confused. On Wikipedia there are lots of different definitions of the phase and I didn't know which one suits. – user501436 Nov 15 '17 at 15:38
  • Ah, so it sounds to me like your teacher is describing a "harmonic oscillator": https://en.wikipedia.org/wiki/Harmonic_oscillator#Simple_harmonic_oscillator – user143410 Nov 15 '17 at 15:51

1 Answers1

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Phase means how far an oscillation has gotten through its cycle. There are various ways of expressing this. You could use a fraction - eg it is 1/4 way through its cycle.

Cycles suggest moving in a circle so it is convenient to compare different kinds of oscillations with motion in a circle with uniform speed, even when the oscillation is actually in a straight line, or when there is no "motion" at all (eg an oscillation of potential difference in an electric circuit). Referring to the circle, 1/4 way through the cycle is $90^{\circ}$. Using radians has a number of advantages over using degrees mathematically, so radians is preferred.

enter image description here Image courtesy of SlideShare

The connection between circular motion and linear harmonic oscillation is that if you project the motion of an object P rotating around a circle of radius $A$ onto the horizontal or vertical axis, then the motion of the object's "shadow" Q along the axis is described by $y=A\sin(\omega t)$ or $x=A\cos(\omega t)$. Here $t$ is time and $\omega t=\theta$ is the "phase" or reference angle, ie the instantaneous angle between the x axis and the radius from the origin to the object P.

$\omega$ is the angular frequency. Frequency $f$ is how many times the object rotates round the circle every second, or how many times an oscillation goes through a full cycle every second. Angular frequency is how many times the object rotates through 1 radian every second, or how many times the oscillation goes through a fraction of $\frac{1}{2\pi}$ of a complete cycle every second. A full circle is $2\pi$ radians so angular frequency is related to frequency by $\omega=2\pi f$.

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