Understanding Wave Graphs: 4t & 30° Phase Angle

[Maxwell]

Lately, I have been trying to get a deeper understanding of a few concepts, and I was trying to analylize a wave I found in my textbook:

I know the sinusoidal equation is:

$Vs = Vm*sin({\omega}t + {\phi})$

The equation for the given wave is:

$Vs = Vm*sin(4t + 30^o)$

My question is how does the 4t change this graph? Also, What does the phase angle change*?

If the equation was just $Vs = Vm*sin(4t)$, how would the graph change?

Thank you!

PS - Please excuse the terrible mspaint graph!

 

[Ethers0n]

Well, I may be very wrong, but the angle is the phase angle of the sinusoid. This comes into play when dealing with power factors. ie, phase matching.
hope this sheds some light...


(take everything with a grain of salt, it tastes better that way)

 

[willib]

Lately, I have been trying to get a deeper understanding of a few concepts, and I was trying to analylize a wave I found in my textbook:

I know the sinusoidal equation is:

$Vs = Vm*sin({\omega}t + {\phi})$

The equation for the given wave is:

$Vs = Vm*sin(4t + 30^o)$

My question is how does the 4t change this graph? Also, What does the phase angle change*?

If the equation was just $Vs = Vm*sin(4t)$, how would the graph change?

Thank you!

PS - Please excuse the terrible mspaint graph!

you need to understand the relationship between radians and degrees..
${\omega}=2{\pi}/t$ radians /sec
and how to convert between the two.. and where each one is on the graph ..

 

[EvLer]

My question is how does the 4t change this graph? Also, What does the phase angle change?
If the equation was just $Vs = Vm*sin(4t)$, how would the graph change?

Actually the graph you attached explains it all.
Phase is basically offset of the regular sin(x) or cos(x), i.e. shift along the horizontal axis. While angular velocity/frquency (w = 4t) is the frequency of the signal, i.e. if it were just t, the sinusoidal graph would have just one wave-length through the period of 2pi, for 4t crudely speaking, you have 4 wave-lengths crammed into segment of 2pi.
So, I would read-up on basic relationship of frequency/period and how f(x) behaves: f(cx), f(x + c) and so on, it's explained in Calculus I.

 

[Delta]

It maybe worth looking into this deeper to show how different variables act on the wave.

Take the formula $Vs = A*sin({\omega}t + {\phi})+C$

The A is the amplitude and represents the different between the upper and lower peaks.

The $\omega$ is the angular velocity: $\omega = 2{\pi}f = 2{\pi}/T$

The $\phi$ is the phase angle, i.e. the horizontal offset graphically speaking.

The C is the vertical offset from the x-axis, usually defined as the DC element of the waveform (in electronics).