will be essentially given by equation (12.1). 
Waves in water of constant depth: 
Consider a point in the transition zone where the depth is con- 
stant over a rather large area. The problem is to represent the sea 
surface and the other desired quantities in the vicinity of that 
point. None of the previous representations are correct in the tran- 
sition zone except that the wave record as a function of time is 
still given by the same general function of time discussed in Chapter 
7. In particular the methods given in Chapter 10 for the determi- 
nation of power spectra as a function of w and 0, will not apply to 
waves measured in the transition zone. 
Eouation (12.1) gives the speed of the wave crests as a function 
of the wave length for a pure sine wave in water of depth, H. Equa- 
tion (12.2) relates the speed of the wave crests to the wave length 
and the wave period. The period is independent of depth. From equa- 
tion (12.1) and (12.2), an equation for the wave length of a wave in 
water of depth H can be found in terms of the wave period. A con- 
version of spectral periods to spectral frequencies then will permit 
integrals over power spectra similar to those considered before. 
If the expression for C in terms of L and # in equation (12.2) 
is substituted into equation (12.1), equation (12.3) is the result. 
Rearrangement then yields equation (12.4) in which the wave length 
in water of depth, H, is given as a function of the spectral fre- 
quency and the depth. 
Usually (12.4) has been solved graphically (with a slightly 
different notation). Sverdrup and Munk [1944] give graphs of L/L, 
(i.e. Le/2npee) as a function of arH/L,- The Beach Erosion Board 
28 
