# Harmonic plane wave

1. Oct 30, 2012

### Tosh5457

Hi, why does the harmonic plane wave have the form below:

$$V(r,t)= acos[\omega (t-\frac{r\cdot s}{v})+\delta ]$$

(r is the position vector, s is the vector that points to the direction the wave is propagating, v is the wave propagation velocity and delta is the phase constant).

2. Oct 30, 2012

### andrien

it just comes out by solving the wave eqn
2v=∂t2v,where c=1 I have put.
You can use spherical coordinates to get it,but more simple would be cartesian coordinate and then using the method of separation of variables, you can get it.

3. Oct 30, 2012

### pabloenigma

More simply, any function that represents a traveling wave is a function of r.s-vt,ie f(r.s-vt)(r and s are vectors ofcourse). If a harmonic function travels as a wave,then the nature of the function is harmonic,ie sine or cosine.

4. Apr 5, 2013

### Francessca

what is the definition of a plane harmonic wave?

5. Apr 5, 2013

### vanhees71

Using spherical coordinates gives you the spherical harmonics and spherical Bessel functions, not the plane wave. Separation in Cartesian coordinates gives plane waves.

6. Apr 5, 2013

### sophiecentaur

It's just a posh way of describing a simple wave for which the displacement at any given time is the same over a plane (at right angles to the direction of propagation). It's the same expression as you get for a wave on a one dimensional string and is the limit for spherical wave at a great distance from the source. It's a very convenient approximation to use.