June 10th, 2019, 10:06 AM  #1 
Member Joined: Aug 2017 From: India Posts: 53 Thanks: 2  Phasor Representation of sine wave
I don't understand why Sine wave should be represented as a phasor, that is, as a circle with a rotating vector. Why should it be rotating at angular speed (omega)? This is an additional item that confuses me. Suppose in the picture I am assuming it is moving at some speed; if it runs at twice the speed, how does the waveform will look like? I know the questions are not clear, but how I do I link omega, t, frequency?
Last edited by skipjack; June 11th, 2019 at 04:28 AM. 
June 11th, 2019, 04:40 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,746 Thanks: 2133 
The sine wave doesn't need to be related to a rotating vector. Although the diagram refers to the time domain, the horizontal axis for the sine wave uses ωt, which is dimensionless and corresponds to an angle in the lefthand diagram (if ω isn't zero). The word "frequency" relates to how often something occurs. If you choose to consider a vector that rotates at a constant nonzero rate, it's convenient to draw a horizontal axis that aligns with the vector at time zero. If that alignment occurs n times per second, it would be reasonable to refer to "n times per second" as the frequency of the rotation. After t seconds have elapsed, the vector has rotated through 2$\pi$n radians, so ω = 2$\pi$n. You asked how the waveform looks if the frequency is changed. What the waveform "looks like" depends on the scaling used for drawing it. If the frequency is changed and a corresponding change is made to the scaling, the waveform will look the same. 
June 11th, 2019, 07:38 AM  #3 
Member Joined: Aug 2017 From: India Posts: 53 Thanks: 2  

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phasor, representation, sine, wave 
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