TI-80 and TI-84 Plus CE – Two Opposing Ocean Waves
The program OPPTIDE draws an ocean wave consisting of a composite of two opposite waves at time t seconds.
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
G ≈ 32.174049 ft/s^2 (approximate Earth’s gravitation constant)
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))
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”
TI-84 Plus CE Program OPPTIDE
0→Xmin: 50→Xmax: 5→Xscl
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
√(G K * tanh(KH))→W
“A cos(KX – WT) + A cos(KX + WT)” → Y1
At T = 1 second with parameters:
W = 75.5 feet
A = 4.76 feet
H = 25 feet
See the results below.
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
This blog is property of Edward Shore, 2018.