From Table C-l of Appendix C, entering with d/L^,
— = 0.07712 ,
L
hence
40
(0.07712)
519 feet ,
and
/2irà\
cosh I---- ) = 1.1197 .
\ L /
Therefore, from Equation 2-29
cosh [2ff(z + d)/L]
cosh [2tt(— 38 + 40)/519] _ 1.0003
n
_
cosh (2nd/L)
“
1.1197
1.1197 '
Since n = a = H/2 when the pressure is maximum (under the wave crest),
and N = 1.0 since linear theory is assumed valid,
H _ N (p 4- pgz)
2 "
PgK2
1.0 [2590 + (64.4) (- 38)]
(64.4) (0.8934)
2.47 feet
Therefore,
H = 2 (2.47) ~ 5 feet .
Note that the tabulated value of K in Appendix C, Table C-l, could not
be used since the pressure was not measured at the bottom.
*************************************
2.237 Velocity of a Wave Group. The speed with which a group of waves
or a wave train travels is generally not identical to the speed with which
individual waves within the group travel. The group speed is termed the
group velocity, C • the individual wave speed is the phase velocity or
wave celerity given by Equations 2-2 or 2-3. For waves propagating in
deep or transitional water with gravity as the primary restoring force,
the group velocity will be less than the phase velocity. (For those waves
propagated primarily under the influence of surface tension, i.e., capillary waves, the group velocity may exceed the velocity of an individual
wave.)
The concept of group velocity can be described by considering the
interaction of two sinusoidal wave trains moving in the same direction
2-24