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k is the wave number: k = 2π/λ (radians per meter), ω is the angular frequency: ω = 2π/T (radians per second), x is the horizontal coordinate and the wave propagation direction (meters), z is the vertical coordinate, with the positive z direction pointing out of the fluid layer (meters), λ is the wave length (meters), T is the wave period .
When two signals with these waveforms, same period, and opposite phases are added together, the sum + is either identically zero, or is a sinusoidal signal with the same period and phase, whose amplitude is the difference of the original amplitudes. The phase shift of the co-sine function relative to the sine function is +90°.
The units of the amplitude depend on the type of wave, but are always in the same units as the oscillating variable. A more general representation of the wave equation is more complex, but the role of amplitude remains analogous to this simple case. For waves on a string, or in a medium such as water, the amplitude is a displacement.
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