# Putting together a wave function from given data

1. Oct 17, 2007

### Pyrestrike

Hi all, I've got a question I think I understand conceptually but not mathematically...

1. The problem statement, all variables and given/known data
A transverse sinusoidal wave on a string has a period T = 25.0 ms and travels in a negative x direction with a speed of 30.0 m/s.
At t=0, a particle on the string at x=0 has a transverse position of 2.00 cm and is traveling downward with a speed of 2.00 m/s.

So, I put together the given data as:

T = 0.025 s
v = 30.0 m/s
y' = 0.02 m
x' = 0m
t' = 0s
v(tangent) = -2.00 m/s

* the (') denotes initial condition

2. Relevant equations
a) What is the amplitude of the wave?
b) What is the initial phase angle?
c) What is the maximum transverse speed of the string?
d) Write the wave function for the wave.

3. The attempt at a solution
a) Okay, so my initial (and really only) idea on how to tackle finding amplitude is:

EQ 1
y = A sin (kx - ωt)

where A is amplitude, k is the wave number, omega is angular frequency, and t is time. I want to use the initial conditions y', x', and t' to try and find A, since they're all given and the latter two equal 0, but I found that would make sin(0), which is undefined. From there, I really don't know if I'm even on the right track for finding A, or if there is a formula that I'm missing to help find it.

b) I would use the general expression of the above sinusoidal wave, where phi is attached to the end of the sine function. The only problem is that again A needs to the found.

c) Finding v(max) would just be using the velocity of an object in harmonic motion:

EQ 2
v = -ω A sin *(ωt + Φ)

d) This is obviously just plugging in the appropriate values into EQ 1

--

My big problem is just where to start (unless there's something wrong with my logic on the other three parts). I have an inclination that I need to solve for λ, k, and ω using the following equations:

EQ3: λ = vT
EQ4: k = (2π) / λ
EQ5: ω = (2π) / T

But I don't know how to apply them to finding A, so in the end I'm still in a confused mess. Can anyone guide me in at what I might be missing?

--Brian

Last edited: Oct 17, 2007
2. Oct 18, 2007

### learningphysics

I'd simply try to find the wave equation instead of going through the parts bit by bit... once you have the equation, you can simply answer all the questions...

The general wave equation is:

y = A sin (kx - ωt + phi)

you can get w immediately from T... like you showed using w = 2*pi/T. Then you can also get k, using v = w/k. v is given as -30.

so now you're left with getting A and phi.

y = A sin (kx - ωt + phi)
dy/dt = -wAcos(kx - wt + phi)

you're given y and dy/dt at t = 0, x = 0... plug into the above equations... then you have 2 equations with 2 unknowns. solve for A and phi.

3. Oct 18, 2007

### Pyrestrike

Gah! Wow, I've gotten the whole "do things in order" bit by my past physics teachers that I didn't even think of that... Thanks muchly!