Fdtxjr

How to handle characters who are more educated than the author?

Can I visit the Trinity College (Cambridge) library and see some of their rare books

Why can't devices on different VLANs, but on the same subnet, communicate?

What force causes entropy to increase?

"... to apply for a visa" or "... and applied for a visa"?

How did passengers keep warm on sail ships?

The following signatures were invalid: EXPKEYSIG 1397BC53640DB551

Word for: a synonym with a positive connotation?

What happens to a Warlock's expended Spell Slots when they gain a Level?

Am I ethically obligated to go into work on an off day if the reason is sudden?

What aspect of planet Earth must be changed to prevent the industrial revolution?

Make it rain characters

Mortgage adviser recommends a longer term than necessary combined with overpayments

What can I do if neighbor is blocking my solar panels intentionally?

One-dimensional Japanese puzzle

What is the role of 'For' here?

Sort list of array linked objects by keys and values

Word to describe a time interval

What was the last x86 CPU that did not have the x87 floating-point unit built in?

Homework question about an engine pulling a train

Can each chord in a progression create its own key?

Sub-subscripts in strings cause different spacings than subscripts

For what reasons would an animal species NOT cross a *horizontal* land bridge?

Why don't hard Brexiteers insist on a hard border to prevent illegal immigration after Brexit?

Why is this plotted summation of two sine functions not eveloped?

0

$begingroup$

I am simply plotting a sum of two different sine waves:

$$x(t)=asin(omega_0t)+bsin((1+epsilon)omega_0t)$$

According to this article about beat, the sum should be an enveloped sine wave:

However, when I do this myself, the result is different:

I notice the red sum wave simply has the frequency of the higher frequency wave, and its amplitude's pattern follows the amplitude's pattern of the other one, not oscillates between $pm g(t)=pmsqrta^2+b^2+2*a*b*cos(epsilonomega_0*t)$ as it theoretically should be.

Where did I do wrong? Here are the code input for MathStudio:

Slider([b, e], .1, 10, 0.1)
w=1;a=1
Plot(a*sin(w*x), color=PaleGreen)
Plot(b*sin((1+e)*w*x), color=LightBlue)
Plot(a*sin(w*x)+b*sin((1+e)*w*x), color=Crimson)
/*Plot(sqrt(a^2+b^2+2*a*b*cos(e*w*x)) */

trigonometry summation

share|cite|improve this question

edited Mar 24 at 17:56

J. M. is not a mathematician

61.2k5152291

asked Jul 1 '17 at 20:29

OokerOoker

349319

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You should see the effect if you make $epsilon << 1$
  $endgroup$
  – WW1
  Jul 1 '17 at 20:41
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  When the two sine waves have almost the same frequency you get the upper graph. When one has much lower frequency than the other you get the lower graph.
  $endgroup$
  – md2perpe
  Jul 1 '17 at 23:35
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @WW1 why does that happen? The article uses $epsilon=0.1$, which I also used, but I didn't see the expected result.
  $endgroup$
  – Ooker
  Jul 2 '17 at 4:52
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Why do you say you used the same number as the article? $10 neq 0.1.$ If you have another attempt with the slider at the far left (so that $e = 0.1$) then you should be showing us that attempt instead of the one with $e=10.$
  $endgroup$
  – David K
  Mar 24 at 19:22
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @DavidK sorry. At the time of posting I don't know the importance of $epsilon$, so I just pick a random graph.
  $endgroup$
  – Ooker
  Mar 25 at 0:09
  
  

  
  
  
  

add a comment | 

0

$begingroup$

I am simply plotting a sum of two different sine waves:

$$x(t)=asin(omega_0t)+bsin((1+epsilon)omega_0t)$$

According to this article about beat, the sum should be an enveloped sine wave:

However, when I do this myself, the result is different:

I notice the red sum wave simply has the frequency of the higher frequency wave, and its amplitude's pattern follows the amplitude's pattern of the other one, not oscillates between $pm g(t)=pmsqrta^2+b^2+2*a*b*cos(epsilonomega_0*t)$ as it theoretically should be.

Where did I do wrong? Here are the code input for MathStudio:

Slider([b, e], .1, 10, 0.1)
w=1;a=1
Plot(a*sin(w*x), color=PaleGreen)
Plot(b*sin((1+e)*w*x), color=LightBlue)
Plot(a*sin(w*x)+b*sin((1+e)*w*x), color=Crimson)
/*Plot(sqrt(a^2+b^2+2*a*b*cos(e*w*x)) */

trigonometry summation

share|cite|improve this question

edited Mar 24 at 17:56

J. M. is not a mathematician

61.2k5152291

asked Jul 1 '17 at 20:29

OokerOoker

349319

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You should see the effect if you make $epsilon << 1$
  $endgroup$
  – WW1
  Jul 1 '17 at 20:41
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  When the two sine waves have almost the same frequency you get the upper graph. When one has much lower frequency than the other you get the lower graph.
  $endgroup$
  – md2perpe
  Jul 1 '17 at 23:35
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @WW1 why does that happen? The article uses $epsilon=0.1$, which I also used, but I didn't see the expected result.
  $endgroup$
  – Ooker
  Jul 2 '17 at 4:52
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Why do you say you used the same number as the article? $10 neq 0.1.$ If you have another attempt with the slider at the far left (so that $e = 0.1$) then you should be showing us that attempt instead of the one with $e=10.$
  $endgroup$
  – David K
  Mar 24 at 19:22
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @DavidK sorry. At the time of posting I don't know the importance of $epsilon$, so I just pick a random graph.
  $endgroup$
  – Ooker
  Mar 25 at 0:09
  
  

  
  
  
  

add a comment | 

$begingroup$

I am simply plotting a sum of two different sine waves:

$$x(t)=asin(omega_0t)+bsin((1+epsilon)omega_0t)$$

According to this article about beat, the sum should be an enveloped sine wave:

However, when I do this myself, the result is different:

I notice the red sum wave simply has the frequency of the higher frequency wave, and its amplitude's pattern follows the amplitude's pattern of the other one, not oscillates between $pm g(t)=pmsqrta^2+b^2+2*a*b*cos(epsilonomega_0*t)$ as it theoretically should be.

Where did I do wrong? Here are the code input for MathStudio:

Slider([b, e], .1, 10, 0.1)
w=1;a=1
Plot(a*sin(w*x), color=PaleGreen)
Plot(b*sin((1+e)*w*x), color=LightBlue)
Plot(a*sin(w*x)+b*sin((1+e)*w*x), color=Crimson)
/*Plot(sqrt(a^2+b^2+2*a*b*cos(e*w*x)) */

trigonometry summation

share|cite|improve this question

edited Mar 24 at 17:56

J. M. is not a mathematician

61.2k5152291

asked Jul 1 '17 at 20:29

OokerOoker

349319

$endgroup$

Slider([b, e], .1, 10, 0.1)
w=1;a=1
Plot(a*sin(w*x), color=PaleGreen)
Plot(b*sin((1+e)*w*x), color=LightBlue)
Plot(a*sin(w*x)+b*sin((1+e)*w*x), color=Crimson)
/*Plot(sqrt(a^2+b^2+2*a*b*cos(e*w*x)) */

share|cite|improve this question

edited Mar 24 at 17:56

J. M. is not a mathematician

61.2k5152291

asked Jul 1 '17 at 20:29

OokerOoker

349319

share|cite|improve this question

edited Mar 24 at 17:56

J. M. is not a mathematician

61.2k5152291

asked Jul 1 '17 at 20:29

OokerOoker

349319

edited Mar 24 at 17:56

J. M. is not a mathematician

61.2k5152291

edited Mar 24 at 17:56

J. M. is not a mathematician

61.2k5152291

asked Jul 1 '17 at 20:29

OokerOoker

349319

asked Jul 1 '17 at 20:29

OokerOoker

349319