Need a little intuition on equation of travelling wave .

[nishantve1]

So here's the equation
y(x,t) = A cos (kx - wt)
where A is the amplitude of vibration and k = 2pi/lambda
i have already dealt with SHM or SHO and i completely understand the equations like
x = Acos(wt + phi)
but i didnt really dealt with waves and the equation of traveling wave is kinda difficult to understand so if someone could I don't know prove or explain how the equation works i would be really happy
thanks in advance

 

[HallsofIvy]

Look at t= 0, x= 0. From that equation, y(0, 0)= A. Now suppose t is a little greater than 0. We can still get y(x, t)= A, as long as kx- wt= 0 which is the same as x= (w/k) t. That is, as long as we are "moving" at speed w/k. Choosing any other value of x with t= 0, we would get some other value of y, less than A, but we could get that same y value by keeping x= that original value of x plus (w/k)t. That is, if we were to move along the x-axis at speed w/k, we would always see exactly the same thing- we would be moving with the wave.