General wave equation conceptual questions

1. Apr 27, 2015

ColtonCM

1. The problem statement, all variables and given/known data

The general wave equation can be shown as: y(x,t) = ymsin(kx-ωt)

2. Relevant equations

See above

3. The attempt at a solution

My question relates to the variables present in this equation. I understand what the amplitude is, its the magnitude of the maximum displacement of elements from their equilibrium position as a wave passes through them.

I understand that the y(x,t) term is the displacement of an element x-distance along the waves travel at time t.

I understand that the x inside the argument of the function describes which element is being looked at along the wave's travel.

I understand that the phase of the equation is the argument of the sine function. Where I get conceptually confused is the other terms inside the phase.

My book describes k as the angular wave number: k = 2π/λ. Can anyone here give me a more general or conceptual description of what k is as a physical property of the traveling wave?

Likewise, I know that ω is angular frequency. I know that the ω is related to period by ω = 2π/T, so similarly T = 2π/ω. So the same question above applies, what is ω as a property of the wave, what is it describing?

Thank you,

Colton

2. Apr 27, 2015

paisiello2

k and ω are simply scale factors for the variables x and t.

The frequency of a sine wave function is the distance between the wave's crests (or also troughs). Therefore k can be thought of as the spatial frequency and ω as the time frequency of the wave i.e. a scaling factor when measuring the distance between crests (or troughs).

The measurement of speed is distance divided by time. So for a wave the distance is the measured distance between any two crests (or troughs) divided by the time for the wave to travel between these two points. This gives the speed of the wave then:
v = (1/k)/(1/ω) = ω/k

Last edited: Apr 27, 2015
3. Apr 27, 2015

Staff: Mentor

I think you meant to have the word time rather than distance (the word I bolded).

4. Apr 27, 2015

paisiello2

I guess I meant "value" → length value for x and time value for t.

5. Apr 29, 2015