Amplitude and Velocity of Component Waves

[Okazaki]

Homework Statement

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?

Homework Equations

y'(x,t) = [2y_msin(kx)]*cos(ωt)

The Attempt at a Solution

...I'm honestly not too sure here. See, I know that the equations match up so that:

2y_m = 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?

 

[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 traveling waves in the same terms as the standing wave.

 

[Okazaki]

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 traveling waves in the same terms as the standing wave.

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

 

[BvU]

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

Check out how Two sine waves traveling 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

 

[Okazaki]

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

Check out how Two sine waves traveling 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

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

 

[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 ?