Mixing
Sum of Cosine Waves
0
$begingroup$
Plot two waves on excel: $cos(f_1)$ and $cos(f_2)$ and their sum $[cos(f_1) + cos(f_2)]$.
The frequencies of the waves are $f_1= 2pi*f$ and $f_2= 2 pi*f*(1.1)$. Assume $f=1$
My question is how do we find the sum of 2 waves? and if there is a third wave $cos(f_3)$ with $f_3= 2 pi*f*(1.2)$. How do we find the sum of 3 waves?
trigonometry wave-equation
edited Jan 22 at 0:34
bjcolby15
1,47611016
asked Jan 21 at 22:52
Daniel VoDaniel Vo
1
$endgroup$
|
show 3 more comments
0
$begingroup$
Plot two waves on excel: $cos(f_1)$ and $cos(f_2)$ and their sum $[cos(f_1) + cos(f_2)]$.
The frequencies of the waves are $f_1= 2pi*f$ and $f_2= 2 pi*f*(1.1)$. Assume $f=1$
My question is how do we find the sum of 2 waves? and if there is a third wave $cos(f_3)$ with $f_3= 2 pi*f*(1.2)$. How do we find the sum of 3 waves?
trigonometry wave-equation
edited Jan 22 at 0:34
bjcolby15
1,47611016
asked Jan 21 at 22:52
Daniel VoDaniel Vo
1
$endgroup$
$begingroup$
Please format with MathJax
$endgroup$
– J. W. Tanner
Jan 21 at 22:55
2
$begingroup$
There's not really much to do. The result of adding two cosines is a sum of two cosines, that's simple enough. But you can turn it into a product of two cosines if that seems simpler or more useful to you (en.wikipedia.org/wiki/…). Also, I assume $f$ is your "time" parameter here - in that case, the frequency of the first is $1$ and second $1.1$ (the frequency is not the thing that changes, but the thing that multiplies it to set how fast it's oscillating).
$endgroup$
– orion
Jan 21 at 22:57
$begingroup$
For example if First wave cos(0) = 1 and the second wave cos(0) = 1 their sum is 2. But my professor showed me he still got the sum of them two waves is 1 so I’m confused
$endgroup$
– Daniel Vo
Jan 21 at 23:06
$begingroup$
That's clearly not true, maybe he was mistaken, or you missed a 1/2, or he was discussing a product? But it's still unclear what's the frequency, and what's the "time" or whatever parameter you want. You state f=1, there are no variables left if you do that.
$endgroup$
– orion
Jan 21 at 23:09
$begingroup$
Presumably there’s an $x$ or a $t$ in there somewhere, otherwise you’re asking about the sum of two constants.
$endgroup$
– amd
Jan 21 at 23:10
|
show 3 more comments
0
0
0
$begingroup$
Plot two waves on excel: $cos(f_1)$ and $cos(f_2)$ and their sum $[cos(f_1) + cos(f_2)]$.
The frequencies of the waves are $f_1= 2pi*f$ and $f_2= 2 pi*f*(1.1)$. Assume $f=1$
My question is how do we find the sum of 2 waves? and if there is a third wave $cos(f_3)$ with $f_3= 2 pi*f*(1.2)$. How do we find the sum of 3 waves?
trigonometry wave-equation
edited Jan 22 at 0:34
bjcolby15
1,47611016
asked Jan 21 at 22:52
Daniel VoDaniel Vo
1
$endgroup$
Plot two waves on excel: $cos(f_1)$ and $cos(f_2)$ and their sum $[cos(f_1) + cos(f_2)]$.
The frequencies of the waves are $f_1= 2pi*f$ and $f_2= 2 pi*f*(1.1)$. Assume $f=1$
My question is how do we find the sum of 2 waves? and if there is a third wave $cos(f_3)$ with $f_3= 2 pi*f*(1.2)$. How do we find the sum of 3 waves?
trigonometry wave-equation
trigonometry wave-equation
edited Jan 22 at 0:34
bjcolby15
1,47611016
asked Jan 21 at 22:52
Daniel VoDaniel Vo
1
edited Jan 22 at 0:34
bjcolby15
1,47611016
asked Jan 21 at 22:52
Daniel VoDaniel Vo
1
edited Jan 22 at 0:34
bjcolby15
1,47611016
edited Jan 22 at 0:34
bjcolby15
1,47611016
edited Jan 22 at 0:34
bjcolby15
1,47611016
1,47611016
asked Jan 21 at 22:52
Daniel VoDaniel Vo
1
asked Jan 21 at 22:52
Daniel VoDaniel Vo
1
asked Jan 21 at 22:52
Daniel VoDaniel Vo
1
1
$begingroup$
Please format with MathJax
$endgroup$
– J. W. Tanner
Jan 21 at 22:55
2
$begingroup$
There's not really much to do. The result of adding two cosines is a sum of two cosines, that's simple enough. But you can turn it into a product of two cosines if that seems simpler or more useful to you (en.wikipedia.org/wiki/…). Also, I assume $f$ is your "time" parameter here - in that case, the frequency of the first is $1$ and second $1.1$ (the frequency is not the thing that changes, but the thing that multiplies it to set how fast it's oscillating).
$endgroup$
– orion
Jan 21 at 22:57
$begingroup$
For example if First wave cos(0) = 1 and the second wave cos(0) = 1 their sum is 2. But my professor showed me he still got the sum of them two waves is 1 so I’m confused
$endgroup$
– Daniel Vo
Jan 21 at 23:06
$begingroup$
That's clearly not true, maybe he was mistaken, or you missed a 1/2, or he was discussing a product? But it's still unclear what's the frequency, and what's the "time" or whatever parameter you want. You state f=1, there are no variables left if you do that.
$endgroup$
– orion
Jan 21 at 23:09
$begingroup$
Presumably there’s an $x$ or a $t$ in there somewhere, otherwise you’re asking about the sum of two constants.
$endgroup$
– amd
Jan 21 at 23:10
|
show 3 more comments
$begingroup$
Please format with MathJax
$endgroup$
– J. W. Tanner
Jan 21 at 22:55
2
$begingroup$
There's not really much to do. The result of adding two cosines is a sum of two cosines, that's simple enough. But you can turn it into a product of two cosines if that seems simpler or more useful to you (en.wikipedia.org/wiki/…). Also, I assume $f$ is your "time" parameter here - in that case, the frequency of the first is $1$ and second $1.1$ (the frequency is not the thing that changes, but the thing that multiplies it to set how fast it's oscillating).
$endgroup$
– orion
Jan 21 at 22:57
$begingroup$
For example if First wave cos(0) = 1 and the second wave cos(0) = 1 their sum is 2. But my professor showed me he still got the sum of them two waves is 1 so I’m confused
$endgroup$
– Daniel Vo
Jan 21 at 23:06
$begingroup$
That's clearly not true, maybe he was mistaken, or you missed a 1/2, or he was discussing a product? But it's still unclear what's the frequency, and what's the "time" or whatever parameter you want. You state f=1, there are no variables left if you do that.
$endgroup$
– orion
Jan 21 at 23:09
$begingroup$
Presumably there’s an $x$ or a $t$ in there somewhere, otherwise you’re asking about the sum of two constants.
$endgroup$
– amd
Jan 21 at 23:10
$begingroup$
Please format with MathJax
$endgroup$
– J. W. Tanner
Jan 21 at 22:55
$begingroup$
Please format with MathJax
$endgroup$
– J. W. Tanner
Jan 21 at 22:55
2
2
$begingroup$
There's not really much to do. The result of adding two cosines is a sum of two cosines, that's simple enough. But you can turn it into a product of two cosines if that seems simpler or more useful to you (en.wikipedia.org/wiki/…). Also, I assume $f$ is your "time" parameter here - in that case, the frequency of the first is $1$ and second $1.1$ (the frequency is not the thing that changes, but the thing that multiplies it to set how fast it's oscillating).
$endgroup$
– orion
Jan 21 at 22:57
$begingroup$
There's not really much to do. The result of adding two cosines is a sum of two cosines, that's simple enough. But you can turn it into a product of two cosines if that seems simpler or more useful to you (en.wikipedia.org/wiki/…). Also, I assume $f$ is your "time" parameter here - in that case, the frequency of the first is $1$ and second $1.1$ (the frequency is not the thing that changes, but the thing that multiplies it to set how fast it's oscillating).
$endgroup$
– orion
Jan 21 at 22:57
$begingroup$
For example if First wave cos(0) = 1 and the second wave cos(0) = 1 their sum is 2. But my professor showed me he still got the sum of them two waves is 1 so I’m confused
$endgroup$
– Daniel Vo
Jan 21 at 23:06
$begingroup$
For example if First wave cos(0) = 1 and the second wave cos(0) = 1 their sum is 2. But my professor showed me he still got the sum of them two waves is 1 so I’m confused
$endgroup$
– Daniel Vo
Jan 21 at 23:06
$begingroup$
That's clearly not true, maybe he was mistaken, or you missed a 1/2, or he was discussing a product? But it's still unclear what's the frequency, and what's the "time" or whatever parameter you want. You state f=1, there are no variables left if you do that.
$endgroup$
– orion
Jan 21 at 23:09
$begingroup$
That's clearly not true, maybe he was mistaken, or you missed a 1/2, or he was discussing a product? But it's still unclear what's the frequency, and what's the "time" or whatever parameter you want. You state f=1, there are no variables left if you do that.
$endgroup$
– orion
Jan 21 at 23:09
$begingroup$
Presumably there’s an $x$ or a $t$ in there somewhere, otherwise you’re asking about the sum of two constants.
$endgroup$
– amd
Jan 21 at 23:10
$begingroup$
Presumably there’s an $x$ or a $t$ in there somewhere, otherwise you’re asking about the sum of two constants.
$endgroup$
– amd
Jan 21 at 23:10
|
show 3 more comments
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$begingroup$
Please format with MathJax
$endgroup$
– J. W. Tanner
Jan 21 at 22:55
2
$begingroup$
There's not really much to do. The result of adding two cosines is a sum of two cosines, that's simple enough. But you can turn it into a product of two cosines if that seems simpler or more useful to you (en.wikipedia.org/wiki/…). Also, I assume $f$ is your "time" parameter here - in that case, the frequency of the first is $1$ and second $1.1$ (the frequency is not the thing that changes, but the thing that multiplies it to set how fast it's oscillating).
$endgroup$
– orion
Jan 21 at 22:57
$begingroup$
For example if First wave cos(0) = 1 and the second wave cos(0) = 1 their sum is 2. But my professor showed me he still got the sum of them two waves is 1 so I’m confused
$endgroup$
– Daniel Vo
Jan 21 at 23:06
$begingroup$
That's clearly not true, maybe he was mistaken, or you missed a 1/2, or he was discussing a product? But it's still unclear what's the frequency, and what's the "time" or whatever parameter you want. You state f=1, there are no variables left if you do that.
$endgroup$
– orion
Jan 21 at 23:09
$begingroup$
Presumably there’s an $x$ or a $t$ in there somewhere, otherwise you’re asking about the sum of two constants.
$endgroup$
– amd
Jan 21 at 23:10