My Math Forum Adding Sin waves

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 March 26th, 2014, 01:08 PM #1 Newbie   Joined: Mar 2014 Posts: 3 Thanks: 0 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
 March 26th, 2014, 01:14 PM #2 Senior Member   Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116 Re: Adding Sin waves You mean if: V1 = 100sin(100t) V2 = 150sin(100t) Then V1 + V2 = 250sin(100t), which has a max of 250.
 March 26th, 2014, 01:46 PM #3 Newbie   Joined: Mar 2014 Posts: 3 Thanks: 0 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.)
 March 26th, 2014, 01:56 PM #4 Senior Member   Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116 Re: Adding Sin waves What sine functions are you trying to add?
 March 26th, 2014, 03:10 PM #5 Newbie   Joined: Mar 2014 Posts: 3 Thanks: 0 Re: Adding Sin waves v1 = 20sin(100?t + 2?/5) v2= 35sin(100?t + 2?/9)
 March 26th, 2014, 06:34 PM #6 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,636 Thanks: 2620 Math Focus: Mainly analysis and algebra 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.

### equation v2 10 sin wt adding v2= 14 sin (wt ԓ/3_)

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