Sinusoidal EK wave equation

[SaintJude]

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So, for those of you have EK and Kaplan, in the Physics chapter on waves you are presented with the equation below on sinusoidal waves. They say we shouldn't memorize it, but understand...well what is this equation saying?!

y(x,t) = A sin (kx-wt) (EK: p.99)

I understand that y(x,t) is referring to the displacement from the equilibrium on a graph of displacement (x) vs. time (t)

And then I'm lost...

 

[davcro]

My way of understanding multivariable formulas is to visualize the plot of the equation will all the variables fixed but one. So for this equation there are two variables, longitudinal displacement (x) and time (t). First plot the equation with time fixed. The wave is frozen in time. As you move down the wave its amplitude will vary like a sine wave. Think waves in the ocean, but frozen in place. As you cross the water goes up and down.

Now plot the equation with x being constant. This would be like floating in one spot in the middle of the ocean. You bob up and down, according to a sine function.

 

[SaintJude]

I wanted to add to this thread b/c there was a Kaplan diagnostic discrete question on it.

Q: A traveling sinusoidal wave is described by

y = 0.01 sin (50x -2t)

in which the numerical constants are in SI units.What are the amplitude and speed of this wave, respectively? Answer = 0.01 m, 0.04 m/s2

The point of this question was to see whether one understood all the components of the wave equation.
The general equation format is Y = Amplitude sin (kx-wt), where K = wave number and w = angular frequency

Well, wavenumber is familiar from spectroscopy and it's k = 2π / λ; and w=2pf. That's what you need to know for this problem.

Then after solving for lambda you'll be able to use v= f λ , wave velocity is then found.

 

[7175pank]

So, for those of you have EK and Kaplan, in the Physics chapter on waves you are presented with the equation below on sinusoidal waves. They say we shouldn't memorize it, but understand...well what is this equation saying?!

y(x,t) = A sin (kx-wt) (EK: p.99)

I understand that y(x,t) is referring to the displacement from the equilibrium on a graph of displacement (x) vs. time (t)

And then I'm lost...

y= position
x = distance
t = time

In other words, when you start at distance (x) your point is at position 👍 when this much time has passed (t).

So, position is a function of your starting point and the time.

 

[shenf1]

I wanted to add to this thread b/c there was a Kaplan diagnostic discrete question on it.

Q: A traveling sinusoidal wave is described by

y = 0.01 sin (50x -2t)

in which the numerical constants are in SI units.What are the amplitude and speed of this wave, respectively? Answer = 0.01 m, 0.04 m/s2

The point of this question was to see whether one understood all the components of the wave equation.
The general equation format is Y = Amplitude sin (kx-wt), where K = wave number and w = angular frequency

Well, wavenumber is familiar from spectroscopy and it's k = 2π / λ; and w=2pf. That's what you need to know for this problem.

Then after solving for lambda you'll be able to use v= f λ , wave velocity is then found.

If you take the derivative of the wave, you get .0004m/s. How come these 2 different methods result in 2 different answers?