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March 26th, 2014, 01:08 PM   #1
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Adding Sin waves

I have been tasked with finding the maximum voltage or radius (R) from the sum of two sine waves. (angle written as $)


V1=100sin(300t)
V2=150cos (300t)

Using
R sin (wt + $) = a cos(wt) + bsin (wt)

then putting in the values taken from above it becomes
R sin (300t + $) = 150cos(300t) +100sin(300t)

so then
R= ?a^2 + b^2 -----> R= ?150^2 + 100^2
R=180

My question is how does this change if both V1 and V2 use a sin function isstead of the 1 cos and 1 sin function used in the example above?
Thankyou
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March 26th, 2014, 01:14 PM   #2
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Re: Adding Sin waves

You mean if:

V1 = 100sin(100t)
V2 = 150sin(100t)

Then V1 + V2 = 250sin(100t), which has a max of 250.
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March 26th, 2014, 01:46 PM   #3
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Re: Adding Sin waves

Sorry, I got that wrong. Not the maximum voltage, but the length of the maximum phase angle or Radius. (In my two graphs, there is also a phase shift, so the maximum is not simply the two indices added together.)
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March 26th, 2014, 01:56 PM   #4
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Re: Adding Sin waves

What sine functions are you trying to add?
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March 26th, 2014, 03:10 PM   #5
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Re: Adding Sin waves

v1 = 20sin(100?t + 2?/5)
v2= 35sin(100?t + 2?/9)
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March 26th, 2014, 06:34 PM   #6
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Re: Adding Sin waves

v1 = 20sin(100?t + 2?/5) = 20(sin(100?t)cos(2?/5) + cos(100?t)sin(2?/5)) = (20cos(2?/5)sin(100?t) + 20sin(2?/5)cos(100?t)
v2 = 35sin(100?t + 2?/9) = 35cos(2?/9)sin(100?t) + 35sin(2?/9)cos(100?t)

v1 + v2 = (20cos(2?/5) + 35cos(2?/9))sin(100?t) + (20sin(2?/5) + 35sin(2?/9))cos(100?t)

And you are back to your original sort of equation.
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