What Determines the Characteristics and Dynamics of a Wave?

[hotmail590]

Wave formula: y(x,t) = Asin(kx-wt)



[] Which variables (x, t, A, k, w) are independent?

Would k be the only independent variable since it is a constant?
However I am not too sure what exactly does the k represents.
Can someone please clear that up for me?

[] Which of the following are parameters that determine the characteristics of the wave? x only, t only, A only, k only, w only, x and t, w and t, A and k and w.

Would A and k and w determine th characteristics of the wave?
I know that A is the amplitude of the wave and w is the angular frequency
of the wave so those 2 has to be characteristics of the wave.

[] What is the phase of the wave?

That would be (kx-wt) right?

[] What is the wavelength of the wave?

Would that be 2pi/k?

[] What is the period of this wave?

Would that be 2pi/w?

[] How do I find the speed of propagation v of this wave?



Thank you for your help.

 

[hotmail590]

please anyone?

 

[SteveDB]

WAve function components.

Wave formula: y(x,t) = Asin(kx-wt)

A can be a function of both time, and space(A(x,t)) unless specifically stated otherwise. It is typically the amplitude, or height of the wave form.
w (omega) is a radian/second-- angular velocity-- function.
k is the restoring force component for an oscillation. It is also noted to be the wave # in optics. In standard oscillations, it's the above stated item.
I.e., it has the property of pulling the oscillation back to zero. We call is the "spring Constant."

l is the wavelength. It is defined by the values-- 2pi*nu/w

[] Which variables (x, t, A, k, w) are independent?

Would k be the only independent variable since it is a constant?
However I am not too sure what exactly does the k represents.
Can someone please clear that up for me?

[] Which of the following are parameters that determine the characteristics of the wave? x only, t only, A only, k only, w only, x and t, w and t, A and k and w.


Would A and k and w determine th characteristics of the wave?
I know that A is the amplitude of the wave and w is the angular frequency
of the wave so those 2 has to be characteristics of the wave.
Each of the items create a specific aspect to the wave. If any of them are different, you'll have a different form on some level.


[] What is the phase of the wave?

That would be (kx-wt) right?

[] What is the wavelength of the wave?

Would that be 2pi/k?--
look at the units of each element

[] What is the period of this wave?

Would that be 2pi/w?


[] How do I find the speed of propagation v of this wave?

Take the time derivative of A*sin(kx-wt)= -w*A cos(kx-wt)
remember, w = rad/sec. Radians are unitless. A has units of length. the sine function is also unitless. Therefore, -w*A... has units of m/s. In this case, the velocity is negative because the angular velocity is negative.

Thank you for your help.

Each element has specific properties that contribute to the entire wave form. Go back and reread the text you're using.
If it does not adequately describe the wave, locate another source.
Do you have the capacity to graph this wave? Calculator, Maple, Mathmatica, Matlab, etc..?
Pick values for each element, and insert into graph. Change them one at a time, and you'll see how much each affects the total form.

 

[SteveDB]

site for waves, and oscillations

http://hyperphysics.phy-astr.gsu.edu/hbase/permot.html#permot
Hope you find this helpful.