For the Pierson-Moskowitz power spectrum, evaluate numerically the areas under the first 20 frequency bands of width \(\Delta \omega=0.1 \mathrm{rad} / \mathrm{s}\) for (a) \(V=10 \mathrm{~m} / \mathrm{s}\), and (b) \(V=20 \mathrm{~m} / \mathrm{s}\). What conclusions can be drawn regarding the effect of wind speed on the frequency distribution of wind energy for this spectrum? Could similar conclusions have been determined by directly studying the equation for the spectrum?