A community for students.
Here's the question you clicked on:
 0 viewing
baru
 one year ago
anyone familiar with the "phenomenon of beats" in the context of differential equations?
baru
 one year ago
anyone familiar with the "phenomenon of beats" in the context of differential equations?

This Question is Closed

baru
 one year ago
Best ResponseYou've already chosen the best response.0anybody know how to break down the general solution to illustrate beats? \[x= \frac{ \cos \omega_1 t  Acos(\omega_0t\phi ) }{\omega^2_0  \omega_1^2 }\] \[\omega_1= driving frequence\] \[\omega_0= naturaal frequency\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0'beats' occur when we have two sinusoids of similar frequency interfering with one another, seemingly moving in and out of phase with time to constructively/destructively interfere periodically, resulting in a oscillating wave whose amplitude *envelope* is also described by a sinusoid. the basis of 'beats' has to do with the fact we can express the product of \(\sin(\omega_1t),\sin(\omega_2t)\) as: $$\sin(\omega_1 t)\sin(\omega_2 t)=\frac12[\cos((\omega_1\omega_2)t)\cos((\omega_1+\omega_2)t)]$$

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0this is the principle of heterodyning in radio receivers

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0http://www.phy.mtu.edu/~suits/beatgraph.gif http://hyperphysics.phyastr.gsu.edu/hbase/sound/imgsou/beat4.gif

baru
 one year ago
Best ResponseYou've already chosen the best response.0but how can I break down the equations i've typed out into products of 'sin'... the coefficients of both the 'cos' terms are different.

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1Trig identities maybe? Hmm \[\cos(ab)=\cos(a)\cos(b)+\sin(a)\sin(b)\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1Maybe try messing around http://www.purplemath.com/modules/idents.htm here are some identities

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0indeed: $$\cos(\omega_1t)A\cos(\omega_t\phi)$$ the beats occur when the forcing frequency does not match the natural frequency, and instead of consistent constructive interference we move in and out of constructive and destructive interference, resulting in an oscillatory motion with timevarying amplitude which is 'jerky'

baru
 one year ago
Best ResponseYou've already chosen the best response.0i get the idea of mismatched frequency...thats not what i'm talking about. inorder to confirm that the resulting plot is one with the amplitude varying sinusoidally, it has to expressed as a products of "sin" : Asin( )sin( ).
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.