the resultant wave height will be zero. The surface profile made up of the sum of the two sinusoidal waves

is given by Equation II-1-47 and is shown in Figure II-1-6. The waves shown in Figure II-1-6 appear to be

traveling in groups described by the equation of the envelope curves

ηenvelope ' *H *cos π

(II-1-48)

(c) It is the speed of these groups (i.e., the velocity of propagation of the envelope curves) defined in

Equation II-1-48 that represents the group velocity. The limiting speed of the wave groups as they become

large (i.e., as the wavelength *L*1 approaches *L*2 and consequently the wave period *T*1 approaches *T*2) is the

group velocity and can be shown to be equal to

4π*d*

1* L*

1%

' *nC*

(II-1-49)

2* T*

4π*d*

sinh

where

Water Wave Mechanics

II-1-25

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