Expressing waves in complex form

AI Thread Summary
The discussion focuses on expressing two waves in complex form and demonstrating that their resultant can be simplified. The user is attempting to break down the wave equations but struggles with converting them into the required complex representation. They suggest potential forms for the individual waves but express confusion about the next steps and the validity of their approach. Additionally, they seek clarification on expressing sine functions in terms of exponential functions and request resources for better understanding. The conversation highlights the challenges of applying complex analysis to wave equations.
inner08
Messages
48
Reaction score
0
Question:
Two waves have the same amplitude, speed, frequency moving in the same region of space. The resultant wave can be expressed like the sum of two waves: psy(y,t) = Asin(ky+wt) + Asin(ky-wt+pi).

Express each wave individually using the complex representation. Demonstrate, using this representation, that the resultant wave can be expressed such as: psy(y,t)=2Acos(ky)sin(wt).

What is the amplitude at y=0, y=pi/k?


Attempt to answer:

I've tried breaking this problem into pieces. I'm having quite a bit of difficulty converting the wave equations into complex form.

I started by splitting the equation in two.

psi1(y,t) = (ky + wt)
psi2(y,t) = (ky - wt + pi)

From there, I'm not sure what to do. I know that I have to convert it into a form of Ae^i(wt-kx+epsilon).

Would simply be: psy1(y,t) = Ae^i(wt+ky) and psy2(y,t) = Ae^i(-wt+ky) ?

I'm pretty confused about this. I don't know where to go from here or even if what I did has sense to it. Hopefully someone can help me out!
 
Last edited:
Physics news on Phys.org
Anyone?
 
Can you write \sin(\theta) in terms of the exponential function?
 
I think (not sure) that its: 1/2i(e^i(\theta) - e^(-i(\theta)))
 
Would anyone know any websites that could explain the idea behind this because my book is limited when describing this concept?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Superposition of Plane EM Waves Using Complex Notation
Replies
2
Views
1K
Intensity Distribution of Superposition of 2 Waves
Replies
11
Views
2K
Wave function - displacement - transverse wave
Replies
3
Views
2K
How do i know what a function describe a wave?
Replies
2
Views
1K
I Don’t understand the general form of the Sinusoidal Wave Equation
Replies
5
Views
2K
Express the following in the form of a Complex Number
Replies
4
Views
5K
Comparing Radio Waves: Short Wave vs. Phone/Radio
Replies
5
Views
2K
A small misunderstanding about waves
Replies
13
Views
2K
Plane wave in cartesian coordinates
Replies
12
Views
2K
Determining Parameters of a Transverse Harmonic Wave
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top