ben wrote:As the author I understood that Linearized Wave Theory suggested that in deep water wave speed was equal to 1.56 x Period.
high school physics (ahhh - the wave equation) states that v = f x Î». if speed is 1.65 x frequency then the theory ben quoted could be interpreted as giving a fixed wavelength of 1.56m. a longer period = lower frequency and therefore a slower speed. All worked out using high school physics.
however, the theory ben has used is not high school physics. water waves are not progressive waves as you were taught (ie a wave caused either by a short term or fixed frequency disturbance at 0 degrees, 90 degrees or 270 degrees to the direction of propogation,). Water waves are affected by a multitude of external factors (water depth, wind speed, density etc etc). Now i'm not for a minute professing to know the slightest hint of the theory ben uses, but if the wind hits the water at any angle high school physics breaks down. infact, high school physics is buggered unless it involves angles of 0, 90, 180, 270 or 360 degrees. Any other angle means the maths gets horrendous. especially with waves, as if the driving force hits the water at any angle other than those listed above, it will create longitudinal and transvere waveforms in the same space, creating superposition and beat frequencies. Each of these will probably creatle localised currents in the water (gravity will try to pull the top of the wave down, and i reckon this means that the peaks will be accelerating when the troughs are travelling at constant velocity). This will continually affect the shape of the surface, setting up vortexes and eddy currents in the airflow. and its the airflow that creates the wave. Huuuuge feedback going on........or in english a bloody complicated wave. meaning that the 'clean' , ideal and simplistic wave equation that is universally taught breaks down due to the complex disturbance caused. the actual equation ben used (and i can't argue for or against) is velocity equals 1.56 x period. That means that as the constant is 1.56, the velocity is directly proportional to the period, hence a longer period means faster waves. its the theory ben has quoted and if it works and it's simple its usually right........therefore i'd go for bens theory.