How Do You Calculate Wave Speed Using the Wave Equation?

[Ishu]

Wave Equation problem..! Help...!

Hi can anyone solve this??
I couldn't figure out how to use it

Question
Use the wave equation to find the speed of wave given by

y(x,t)=(3.00 mm) sin [(4.00/m)x-(7.0/s)t) ]





I guess the wave equation is ,

(d^2y) 1 (d^2y)
------- = ------ -------
(dx^2) v^2 (dt^2)


can anyone solve it step wise?

 

[Päällikkö]

can anyone solve it step wise?

Not really, no. That's not quite how stuff's done on this forum. You're supposed to do the work yourself.

The wave equation:
$$\frac{\partial ^2 y}{\partial x^2} = \frac{1}{v^2}\frac{\partial ^2 y}{\partial t^2}$$

For the given wave, can you solve
$$\frac{\partial ^2 y}{\partial x^2}$$ and $$\frac{\partial ^2 y}{\partial t^2}$$ ?

 

[Ishu]

I mean need some hint...

please I ahve 1 more hrs left

 

[Ishu]

Am i suppose to t6ake second derivative of whole equation...twice? once with respect to t and again with respect to x?
is that how I am supposed to do?

 

[Päällikkö]

Am i suppose to t6ake second derivative of whole equation...twice? once with respect to t and again with respect to x?
is that how I am supposed to do?

Yep, that's what you're supposed to do.

 

[Ishu]

that means I am supposed to solve for "V" right?

But the answer I got is not the same as the one I got from V=w/k

??

 

[Päällikkö]

that means I am supposed to solve for "V" right?
But the answer I got is not the same as the one I got from V=w/k
??

It should be the same, as the equation reduces to $$v = \frac{\omega}{k}$$