From [FWHM.sub.K] = 2[[sigma].sub.k] [square root of (2 ln 2)] and the relation between the

wavenumber k and wavelength [lambda] the [FWHM.sub.z] is

Caption: Figure 2: Coefficient of [K.sub.R.sup.2] + [K.sub.T.sup.2] + [eta] versus the dimensionless

wavenumber kh.

Again, intensities of the absorptions have been adjusted to clarify positioning along the

wavenumber axis.

In the

wavenumber region of 1900-1300 [cm.sup.-1] the C=O stretching vibration peaks at 1730 [cm.sup.-1] can be found.

For this event we obtain [k.sub.local] = 0.081 [m.sup.-1] and [c.sub.local] = 12.6 m/s (with [U.sub.1] = 1 m/s), which is 10% higher than the linear estimate based on the global

wavenumber of the wave series.

Where R([omega]) is the reflectance and is the phase change between the incident and reflected signals for a particular

wavenumber [omega].

For a given real

wavenumber k, the complex angular frequency can be obtained as [omega] = [[omega].sub.r] + i[[omega].sub.i], by solving a simple polynomial equation of third degree, for which numerical and even closed form solutions exist.

In this case, the C-O-P band shifts to a higher

wavenumber (1122 [cm.sup.-1]) with an increase in intensity and a decrease peak width.

Here we consider the real

wavenumber and find the complex solutions of the frequency as [[omega].sub.r] + i[[omega].sub.i],.

The FTIR instrument operates in a single-beam mode and is capable of data collection over a

wavenumber range of 400-4000 [cm.sup.-1] with a resolution of 0.5 cm Beach sand collected before the BP oil well explosion was used as reference baseline.

The instability regions of a uniform Stokes wave in the perturbed

wavenumber plane obtained from this equation are found to be in better agreement with the exact results of McLean et al.