Two waves Interfereing resulting waves interferes with another wave

  • Thread starter c-murda
  • Start date
  • #1
c-murda
67
0
[SOLVED] Two waves Interfereing...resulting waves interferes with another wave

Homework Statement


Two traveling sinusoidal waves given by

Y1(x,t) = 3.87 sin (2.00x - 40.0t) and Y2(x,t) = 3.87 sin(2.00x - 40.0t + 120deg.)

interfere. The resulting wave interferes with

Y3 ( x, t) = 3.87 sin ( 2.00x- 40.0t)


Homework Equations







The Attempt at a Solution



i am confused...do i add the two first waves together, then add that wave with the third wave? do i need to change my degrees to radians?
 

Answers and Replies

  • #2
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,624
8
Welcome to PF!
i am confused...do i add the two first waves together, then add that wave with the third wave?
Sounds good to me!
do i need to change my degrees to radians?
I shouldn't think so.
 
  • #3
c-murda
67
0
alright so i guess i need to know how to add waves...
 
  • #4
quantumdude
Staff Emeritus
Science Advisor
Gold Member
5,575
23
There are some rather obvious trig identities that you should be using here. Do you have a table of trig identities? If so, can you find one in which two sine functions are being added together?
 
  • #5
c-murda
67
0
i have my physics book which doesn't go to sinusoidal waves
 
  • #6
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,624
8
i have my physics book which doesn't go to sinusoidal waves
Try looking for the angle-sum identity for sine. If you can't find it in your physics text, try a mathematics text or alternatively have a look on the internet :wink:
 
  • #7
c-murda
67
0
thnx... you mean like

sin(A+B) = sinAcosB + cosAsinB

i don't understand how that applies to the waves adding tho
 
  • #8
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,624
8
thnx... you mean like

sin(A+B) = sinAcosB + cosAsinB
Sorry, my bad! I meant sum to product formulae :redface:
i don't understand how that applies to the waves adding tho
Well, your waves are sinusoidal functions aren't they?
 
  • #9
quantumdude
Staff Emeritus
Science Advisor
Gold Member
5,575
23
i have my physics book which doesn't go to sinusoidal waves

I'm talking about trig identities that come from a typical course in College Algebra and Trigonometry or Precalculus. Surely such a math course would be a prerequisite for your physics course?
 
  • #10
c-murda
67
0
ynet(x, t) = y1(x, t) + y2(x, t)

= Asin(wt - kx) + Asin(wt - kx + f)

= [2Acos 1/2(theta)]sin(wt -kx + 1/2 f).
 
Last edited:
  • #11
quantumdude
Staff Emeritus
Science Advisor
Gold Member
5,575
23
And what is "theta"?
 
  • #12
c-murda
67
0
originally its 120 so...theta would be 60 for the first two interference and 30 for the 2nd interference?
 
  • #13
c-murda
67
0
sry i don't why the f's are f's they should be thetas
 
  • #14
quantumdude
Staff Emeritus
Science Advisor
Gold Member
5,575
23
sry i don't why the f's are f's they should be thetas

Right. And it doesn't matter if you call them all f's or thetas, as long as they are the same symbol.

So there is your formula for adding two sinusoidal waves with the same amplitude and frequency, but different phase angles.
 
  • #15
c-murda
67
0
ok so now i have a few more questions about the reamaing part of the problem.

its ask for
amplitude:
2ym cos 120/2 = 2*3.87*cos 60 = 3.87 (interference of 1+2)
2ym cos 60/2 = 2*3.87*cos 30 = 6.70(interference of resultant and 3)

correct?

Phase = 120/2 = 60 (interference of 1+2)
60 / 2 = 30 (interference of resultant and 3)

wavelength = i need help here...isn't it lambda?
defined as 2pi/k

frequency
defined as w = 2piF ; F is frequency?
defined as w = 2pi/T ; since f = 1/T
so F = 1/T

period:


wave number
this is k right?
 
Last edited:
  • #16
c-murda
67
0
i have 715 deadline please help
 
  • #17
quantumdude
Staff Emeritus
Science Advisor
Gold Member
5,575
23
You are correct on all counts.
 
  • #18
c-murda
67
0
period

what about the period
 
  • #19
c-murda
67
0
wavelength = i need help here...isn't it lambda?
defined as 2pi/k

so does that mean the final wavelength will be just pi?

frequency
defined as w = 2piF ; F is frequency?
defined as w = 2pi/T ; since f = 1/T
so F = 1/T

so does that mean final frequency will be 6.36?
period:

wave number
this is k right?

that mean k= 2?
 
  • #20
quantumdude
Staff Emeritus
Science Advisor
Gold Member
5,575
23
Those are all correct. And since you got the frequency, you can easily get the period.
 
  • #21
c-murda
67
0
for the final period would it be .157?
 
  • #22
quantumdude
Staff Emeritus
Science Advisor
Gold Member
5,575
23
Yes indeedy.
 

Suggested for: Two waves Interfereing resulting waves interferes with another wave

  • Last Post
Replies
5
Views
78
Replies
2
Views
363
Replies
5
Views
357
  • Last Post
Replies
4
Views
353
Replies
5
Views
418
Replies
10
Views
314
Replies
5
Views
370
  • Last Post
Replies
1
Views
299
Replies
17
Views
562
Top