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## Homework Statement

Write down an equation to describre a wave [itex]\psi[/itex](x,t) with

**all**of the following properties

a) It is travelling in the negative x direction

b) It has a phase velocity of 2000ms

^{-1}

c) It has a frequency of 100kHz

d)It has an amplitude of 3 units

e) [itex]\psi[/itex](0,0)= 2 units

## Homework Equations

f=[itex]\frac{\omega}{2\pi}[/itex]

[itex]\lambda[/itex]=[itex]\frac{2\pi}{k}[/itex]

v

_{p}=[itex]\frac{\omega}{k}[/itex]

[itex]\psi[/itex](x,t)=Aexp(kx+[itex]\omega[/itex]t)

## The Attempt at a Solution

a) For it to be travelling in the negative x direction the equation would have to be:

[itex]\psi[/itex](x,t)=Aexp(kx-[itex]\omega[/itex]t)

c) For it to have a frequency of 100kHz:

[itex]\omega[/itex]=2[itex]\pi[/itex]f=2*10

^{5}[itex]\pi[/itex]rads

^{-1}

b) For it to have a phase velocity of 2000ms

^{-1}:

v

_{p}=[itex]\frac{\omega}{k}[/itex]

k=[itex]\frac{\omega}{v

_{p}}[/itex]=[itex]\frac{(2*10

^{5})[itex]\pi[/itex]}{2000}[/itex]=100[itex]\pi[/itex]radm

^{-1}

d) For it to have an amplitude of 3 units:

[itex]\psi[/itex](x,t)=3exp[(100[itex]\pi[/itex])x-(2*10

^{5}[itex]\pi[/itex])t]

e) This part I can't work out since I thought if x=0 and t=0 then the answer would just be the amplitude as exp

^{0}=1 but the amplitude is 3 units not 2 so were have I gone wrong here?

Is any of the above correct or have I got it completely wrong? Also if anyone can help me out with part e) that would be great. Finally I don't know why its not including the greek symbols so sorry if it makes anything harder to read like the greek symbols next to the units. Thanks in advance.