Interpreting this wave funtion

[RJS]

Homework Statement

y(x,t)=[(4.8mm)sin(x/3.6m)cos(130rad/s)t]

find Amplitude, wavelength and velocity of wave from the two combined waves.

there are two waves here, combined into one, show each wave function: y1(x,t) and y2(x,t).

Homework Equations

ok, i can fully manipulate the wave function when it's in it's basic form of y(x,t)=Acos(kx-wt+phi) but i must be missing something here. is the problem in a form that can be worked or must it be reworked with a trig function? it's all being multiplied so I'm not sure how to get it into the (kx-wt) format.

any help would be appreciated.

thanks.

The Attempt at a Solution

because they are two waves in this equation Amplitude is (4.8mm/2)=2.4mm... correct?

wave length can be found using kx= [2(pi)x]/(lambda) and velocity will be found using wt=2(pi)tf to find frequency and then v=(lambda)(frequency)

my question is do i need to change the equation? or can i just use it as is?

I don't have the answer to this question, so if you can point me in the right direction?

 

[Redbelly98]

You're correct on amplitude, wavelength, frequency and velocity.

In addition, yes you will need to change the equation, since it asks explicitly to "show each wave function: y1(x,t) and y2(x,t)."

If you can figure out how to express
sin(a)cos(b)
in terms of
sin(a+b), sin(a-b), cos(a+b), and/or cos(a-b)
using trig-addition identities, then it is solvable.

 

[baba89]

As a scientist, it is important to always clarify and fully understand the given information before attempting to solve a problem. In this case, it would be helpful to have a clearer definition of the problem and the context in which it is being presented. It is not clear what the variables x and t represent, and what physical phenomenon the wave function is describing.

However, based on the given information, it seems that there are two waves being combined into one wave function. In order to find the amplitude, wavelength, and velocity of the combined wave, it would be helpful to know the individual wave functions, y1(x,t) and y2(x,t). From there, you can use the basic wave equation, y(x,t) = Acos(kx-wt+phi), to manipulate the given equation and solve for the desired values.

It is also important to note that the given equation is in the form of y(x,t) = Asin(kx)cos(wt), which is different from the basic wave equation. This may require additional steps to manipulate the equation into the desired form.

In general, it is important to have a clear understanding of the variables and equations involved in a problem before attempting to solve it. If there are any uncertainties, it is always best to clarify with the person or source providing the information.