In all but one of these problems all I need is the answers checked. I am uncertain how to do number 5 part b.(adsbygoogle = window.adsbygoogle || []).push({});

1.A wave is traveling 50 m/s to the left(this is a graph) and its wavelength is 10 meters. What is the frequency of the traveling wave?

Answer:v=λ*f; f=5 hertz. Frequency can not be negative, right?

2.What is the speed and direction of the following waves.

ψ(y,t)=A(y-t)^2.Answer: The wave is traveling 1 to the right.

ψ(x,t)=A(Bx+Ct+D)^2. Answer: The wave is traveling at C to the left.

ψ(z,t)=Ae^(Bz^2+BC^2t^2-2BCzt) Answer: Ae^(-B*(z-Ct)^2) The wave is traveling C to the right.

3.A wave of the form y(x,t)=100*sin(2πx-4πt) and you have two detectors to measure the disturbance at points x1=2 and x2=10. What will be the magnitude of the disturbance at x2 the instant t1, when y(x1,t1)=100.

Answer:Knowing that sin(π/2)=1 therefore π/2=4π-4πt; (1-t) = 1/8; t=7/8. Then I plugged t1 = 7/8 into the orginal equation with x2 so y(x2, t1) =~ 70.71.

4.Determine the imaginary part of

Note: The general equation I used for the following part was e^(iθ)=cosθ+i*sinθ and e^(-iθ)=cosθ-i * sinθ

a)z=5*e^(iky)*e^(-iωt)*e^(iε)

Answer: This is what I get for the Imaginary part after some simplifying 5(i*sin(ε)cost(ωt)cos(kx) + i*cos(ε)cos(ωt)sin(kx) + i*cos(ε)sin(ωt)cos(kx) - i*sin(εs)sin(ωt)sin(kx))

b)z=((Ae^(iωt))/(Be^(ikx)))*e^(iε) Answer:I factored out the coeffieceint A/B so I was left with A/B((e^(iωt)* e^(iε)) /e^(ikx) ). Then, I assumed that the entire thing would end up being imaginary, would I be correct in assuming that.

c)z=(Ae^(iωt) + Ae^(-iωt))/2. Answer: When I expapanded this the imaginary parts canceled each other out. So, there would be no imaginary part in this one.

5.Find the magnitude if the complex quantities:

a)ψ(x,t)=e^(ikx)*e^(-iωt)*e^(iε)

Answer: I thought this one was a little to simple, wouldnt it just be equal to 1.

b)ψ(y,t)=2*e^(iky)*e^(iωt) + 4*e^(iky)*e^(-iωt)

Answer: This is the one I am stuck on. This is what I did 2e^(iky)*(e^(iωt)+2e^(-iωt)); 2e^(iky)*(cos(ωt)+i*sin(ωt)+2cos(ωt)-2i*sin(ωt));

2e^(iky)*(3cos(ωt)-isin(ωt))

Then I just didnt know what to do, can you walk me threw how to do this one?

6.There is a wave y=sin(2π(4t-5x+2/3))Find the ...

a)the amplitude, Answer: 1

b)the wavelength, Answer: knowing that this wave is in the form ψ(x,t) = Asin(kx-ωt+ε) then k=10π and ω=8π, then using the formula λ=2π/k=1/5

c)the frequency ω=2πf; f=4hertz

d)the intial phase angle Answer: I guess this would just be the number in the sin if all the variables were zero so it would be 4π/3?

e)the displacement at time t=0 and x=0. Answer: This would just be sin(4π/3)=~.866. Displacement is always postive right?

Thank you for the help.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Optic/Wave Questions

Can you offer guidance or do you also need help?

**Physics Forums | Science Articles, Homework Help, Discussion**