# Two waves Interfereing resulting waves interferes with another wave

[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)

## 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?

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Hootenanny
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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.

alright so i guess i need to know how to add waves...

Tom Mattson
Staff Emeritus
Gold Member
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?

i have my physics book which doesn't go to sinusoidal waves

Hootenanny
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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 thnx... you mean like

sin(A+B) = sinAcosB + cosAsinB

i don't understand how that applies to the waves adding tho

Hootenanny
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thnx... you mean like

sin(A+B) = sinAcosB + cosAsinB
Sorry, my bad! I meant sum to product formulae i don't understand how that applies to the waves adding tho
Well, your waves are sinusoidal functions aren't they?

Tom Mattson
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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?

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).

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Tom Mattson
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And what is "theta"?

originally its 120 so...theta would be 60 for the first two interference and 30 for the 2nd interference?

sry i don't why the f's are f's they should be thetas

Tom Mattson
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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.

ok so now i have a few more questions about the reamaing part of the problem.

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?

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Tom Mattson
Staff Emeritus
Gold Member
You are correct on all counts.

period

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?

Tom Mattson
Staff Emeritus
Gold Member
Those are all correct. And since you got the frequency, you can easily get the period.

for the final period would it be .157?

Tom Mattson
Staff Emeritus