For this case
so (1.33) yields
and (1.34) yields
These are sufficiently simple that one can obtain
explicitly.
From (1.36)
which implies that the local wave length 
increases
with x and decreases with t.
Taking the arbitrary phase constant b = 0, (1.37) and (1.38)
yield
so
which corresponds to a relation given in Art. 238 in Lamb's Hydrodynamics, but arrived at in quite a different manner.
Let n = 
, which when restricted to the
ordinal numbers 1, 2, 3, 
identifies a given wave crest.
From (1.39) we find that
Contours of the wave crests n = 5 to 40 are plotted in Fig. 1
using this relation.
The units of x and t in this plot are taken such that
= 1.
For example, if x has units of 100 m, then t has units of
16 seconds 
.