# Amplitude and Velocity of Component Waves

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1. Apr 28, 2015

### Okazaki

1. The problem statement, all variables and given/known data
A string vibrates according to the equation y(x,t) = 2.0*sin (0.16x)cos (750t) , where x and y are in centimeters and t is in seconds. (a) What are the amplitude and velocity of the component waves whose superposition give rise to this vibration? (b) What is the distance between nodes? (c) What is the velocity of a particle of the string at the position x = 9.0 cm when 3 t 5 10− = × sec?

2. Relevant equations
y'(x,t) = [2ymsin(kx)]*cos(ωt)

3. The attempt at a solution
...I'm honestly not too sure here. See, I know that the equations match up so that:

2ym = 2.0 cm
ω = 750 Hz
k = 0.16m-1

But I'm not sure what to do with this. Does this mean that the original wave(s) that make up this new wave (so the component waves) both had an amplitude of 1.0 cm (and etc.)? Or am interpreting this horribly wrong?

2. Apr 28, 2015

### BvU

Hello there,

If y(x,t) is the superposition of component waves, it should be possible to write y(x,t) as a sum, right ?
Since y(x,t) looks like a standing wave (x and t "oscillate independently"),
it's probably a sum of something that moves in the +x direction and something that moves in the -x direction.

You need expressions for those travelling waves in the same terms as the standing wave.

3. Apr 28, 2015

### Okazaki

That's what I'm struggling with. I don't know how to find it when there's a phase constant.

4. Apr 28, 2015

### BvU

What phase constant ? Are you mixing up with another thread ?

Check out how Two sine waves travelling in opposite directions create a standing wave at Penn State.
Also note that his y(x,t) looks a lot like the one in your exercise.
In fact I am afraid that's already an enormous giveaway.

I don't know at what level you need assistance: are you familiar with the wave equation ? Wavelength, relationships between v (or c), $\lambda$, $\omega$, f, k ?

Note that $\omega$ is not the same as the frequency: f = 750 Hz, but $\omega$ is something else and has a dimension of radians/s

5. Apr 28, 2015

### Okazaki

Oh yes...it appears I am mixing up threads. Sorry about that. :/

6. Apr 28, 2015

### BvU

Well, then I will have to wait patiently...
And before we continue you could perhaps improve on the
3 t 5 10− = × sec​
in the problem statement ?