After the first complété stroke one wave will be
présent and its energy is E/2. One period later this
wave has advanced one wave length but has left onehalf of its energy or E/4 behind. It now occupies a
previously undisturbed area to which it has brought
energy E/4. In the meantime, a second wave has been
generated, occupying the position next to the plunger
where E/4 was left behind by the first wave. The
energy of this second wave equals E/4 + E/2 = 3E/4.
Repeated applications of this reasoning lead to the
results shown in Table 2-1.
The sériés number n gives the total number of
waves présent and equals the time in periods since
the first wave entered the area of calm; the wave
number m gives the position of the wave measured from
the plunger and equals the distance from the plunger
expressed in wave lengths. In any sériés, n, the
déviation of the energy from the value E/2 is
symmetrical about the center wave. Relative to the
center wave ail waves nearer the plunger show an
excess of energy and ail waves beyond the center wave
show a déficit. For any two waves at equal distances
from the center wave the excess equals the deficiency.
In every sériés, n, the energy first decreases slowly
with increasing distance from the plunger, but in the
vicinity of the center wave it decreases rapidly.
Thus, there develops an '‘energy front" which advances
with the speed of the central part of the wave System,
that is, with half the wave velocity.
According to the last line in Table 2-1 a definite
pattern develops after a few strokes: the wave closest
to the plunger has an energy E(2n-l)/2n which approaches
the full amount E, the center wave has an energy E/2,
and the wave which has traveled the greatest distance
has very little energy (E/2n).
Table 2-1. Distribution of Wave Heights in a Short Train of Waves
Sériés
number
n
Wave number, m
Total
energy
of
group
1
2
3
4
5
6
7
1
1/2E — — — — — — 1/2E
2
3/4
1/4E -------- — — — — 2/2
1 3
7/8
4/8
1/8E — — —
______ 3/2
4
15/16
11/16
5/16
1/16E —
—------- — 4/2
31/32
26/32
16/32
6/32
1/32E — ______
5/2
6
| 63/64
57/64
42/64
22/64
7/64
1/64E
6/2
2-32
présent and its energy is E/2. One period later this
wave has advanced one wave length but has left onehalf of its energy or E/4 behind. It now occupies a
previously undisturbed area to which it has brought
energy E/4. In the meantime, a second wave has been
generated, occupying the position next to the plunger
where E/4 was left behind by the first wave. The
energy of this second wave equals E/4 + E/2 = 3E/4.
Repeated applications of this reasoning lead to the
results shown in Table 2-1.
The sériés number n gives the total number of
waves présent and equals the time in periods since
the first wave entered the area of calm; the wave
number m gives the position of the wave measured from
the plunger and equals the distance from the plunger
expressed in wave lengths. In any sériés, n, the
déviation of the energy from the value E/2 is
symmetrical about the center wave. Relative to the
center wave ail waves nearer the plunger show an
excess of energy and ail waves beyond the center wave
show a déficit. For any two waves at equal distances
from the center wave the excess equals the deficiency.
In every sériés, n, the energy first decreases slowly
with increasing distance from the plunger, but in the
vicinity of the center wave it decreases rapidly.
Thus, there develops an '‘energy front" which advances
with the speed of the central part of the wave System,
that is, with half the wave velocity.
According to the last line in Table 2-1 a definite
pattern develops after a few strokes: the wave closest
to the plunger has an energy E(2n-l)/2n which approaches
the full amount E, the center wave has an energy E/2,
and the wave which has traveled the greatest distance
has very little energy (E/2n).
Table 2-1. Distribution of Wave Heights in a Short Train of Waves
Sériés
number
n
Wave number, m
Total
energy
of
group
1
2
3
4
5
6
7
1
1/2E — — — — — — 1/2E
2
3/4
1/4E -------- — — — — 2/2
1 3
7/8
4/8
1/8E — — —
______ 3/2
4
15/16
11/16
5/16
1/16E —
—------- — 4/2
31/32
26/32
16/32
6/32
1/32E — ______
5/2
6
| 63/64
57/64
42/64
22/64
7/64
1/64E
6/2
2-32