**TI-80 and TI-84 Plus CE – Two Opposing Ocean Waves**

**Introduction**

The program OPPTIDE draws an ocean wave consisting of a
composite of two opposite waves at time

*t*seconds.
Inputs:

L = wavelength of the wave in feet (λ)

A = amplitude of the wave in feet

H = depth of the ocean in feet

T = time that the wave is drawn, in seconds

Constants:

G ≈ 32.174049 ft/s^2
(approximate Earth’s gravitation constant)

Output:

Drawing of the wave described by the equation:

y = A cos (K*X – W*T) + A cos (K*X + W*T) (X varies, T is a constant and given), where:

K = 2*π/L

W = √(g*K*tanh(K*H))

Note:

The tanh, hyperbolic tangent function, is not on the
TI-80. Therefore the following definition
is used:

tanh x = (e^(2*x) – 1)/(e^(2*x) + 1)

The tanh function is found only in the catalog of the TI-84
Plus CE ([Shift], [ 0 ]).

**TI-80 Program OPPTIDE**

DISP “2018-01-10 EWS”

RADIAN

0→XMIN

50→XMAN

5→XSCL

32.17049→G

DISP “FEET”

INPUT “WAVELENGTH:”,L

INPUT “DEPTH:”,H

INPUT “AMPLITUDE:”,A

-A-1→YMIN

A+1→YMAX

1→YSCL

INPUT “TIME:”,T

(2π)/L→K

(e^(2KH)-1)/(e^(2KH)+1)→Q

√(QKG)→W

“A*COS(KX-WT)+A*COS(KX+WT)”→Y1

DISPGRAPH

**TI-84 Plus CE Program OPPTIDE**

“EWS 2018-01-10”

Func: Radian

0→Xmin: 50→Xmax: 5→Xscl

32.174049→G

Disp “DISTANCE IN
FEET”

Input “WAVELENGTH:”,
L

Input “AMPLITUDE:”,
A

-A-1→Ymin: A+1→Ymax:
1→Yscl

Input “OCEAN DEPTH:”,
H

Input “TIME (S):”, T

2π/L→ K

√(G K * tanh(KH))→W

“A cos(KX – WT) + A
cos(KX + WT)” → Y1

GraphColor(1,BLUE)

DispGraph

**Example**

At T = 1 second with parameters:

W = 75.5 feet

A = 4.76 feet

H = 25 feet

See the results below.

Source:

Salmon, Rick. “Intro
to Ocean Waves” Scripps Institution of Oceanography. UC San Diego
December 7, 2015. http://pordlabs.ucsd.edu/rsalmon/111.textbook.pdf Retrieved December 26, 2017

Eddie

This blog is property of Edward Shore, 2018.

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