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.