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

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.  

HP Prime and TI-84 Plus CE: Shallow Wave Analysis

HP Prime and TI-84 Plus CE:  Shallow Wave Analysis

Introduction

The program H2OWAVES calculates wave speed, impedance, and wave flux for shallow ocean waves.  The following are assumed:

1. The criteria of λ < D/20 is assumed where λ is the length of the wave.

2. The water assumed to be 0°C, where the density (ρ) is 1,000 kg/m. 

3. SI units are used.  For gravity, g = 9.80665 m/s^2 is used.

Formulas Used

Wave Speed (m/s):  v = √(g * D)

Wave Impedance (Mks):  Z = ρ * v

Wave Energy Flux (W/m):  I = (ρ * g * H)^2/(2 * Z)

Maximum Possible Length (m):  λ = 20 * D

HP Prime Program H2OWAVES

EXPORT H2OWAVES()

BEGIN

// EWS 2017-04-21

// Shallow Wave Analysis

// for D/L<1/20

// SI Units

LOCAL D,H;

LOCAL v,Z,I;

INPUT({D,H},

"Wave Analysis",

{"D: ","H: "},

{"Depth (m)","Wave Height (m)"});

v:=√(9.80665*D);

Z:=1000*v;

I:=(9806.65*H)^2/(2*Z);

PRINT();

PRINT("Wave speed (m/s): "+v);

PRINT("Impedance (Mks): "+Z);

PRINT("Wave Flux (W/m): "+I);

RETURN {v,Z,I};

END;

TI-84 Plus CE Program H2OWAVES

"EWS 2017-04-23"

"SHALLOW WAVES"

"D<F/20"

Disp "SHALLOW WAVES"

Input "DEPTH (M): ",D

Input "HEIGHT (M): ",H

√(9.80665*D)→V

1000*V→Z

(9806.65*H)^2/(2*Z)→I

Disp "WAVE SPEED (M/S):",V

Disp "IMPEDANCE (WKS):",Z

Disp "WAVE FLUX (W/M):",I

Example

Input: 

Depth:  3.2 m

Height:  0.49 m

Output:

Wave Speed: 5.601899678 m/s

Impedance:  5601.899678 Wks

Wave Flux:  2060.953478 W/m

Source:

Ingard, K.U. Fundamental of Waves and Oscillations Cambridge University Press:  New York 1988.  IBSN 0 521 32734

Surf’s up!  Eddie

This blog is property of Edward Shore, 2017.