It is my understanding that the functions used below in the respective Sin[] functions are the standard functions for harmonic waves, transverse waves and standing waves. However, I can only get the harmonic wave to work as expected using the Manipulate[] function. What appears to be happening with the transverse wave is that everything after a plus sign (+) is treated as a phase shift. Please review my code below and tell me what I am missing or what I have wrong.
Plot of Harmonic Motion (Simple Harmonic Motion) - Works as expected
With f = frequency, t = time and b = phase shift
2π is used to convert frequency into radians-per-second
In[]:=
Manipulate[Plot[Sin[2πft+b],{t,0,2}],{f,1,4},{b,0,10}]
Out[]=
​
f
b
0.5
1.0
1.5
2.0
-1.0
-0.5
0.5
1.0
​​​Plot of Transverse Wave - λ and b works as expected, but f and t both work as phase shift which does not work as expected.With λ = wave length in meters, x = distance in meters, f = frequency, t = time and b = phase shift​
2π
λ
x
= Space Component, 2π f t = Time Component and b = phase shift 2π is used to convert frequency into radians-per-second and wavelength (λ) into radians-per-meter
In[]:=
ManipulatePlotSin
2π
λ
x+2πft+b,{x,0,2},{λ,1,4},{f,1,4},{t,1,4},{b,0,10}
Out[]=
​
λ
f
t
b
0.5
1.0
1.5
2.0
-1.0
-0.5
0.5
1.0
Standing Wave function (Superposition of two wavesy[x,t] = (A Sin[κ x - ω t]) - (A Sin[κ x - ω t]) κ x = Space Component, ω t = Time component​With the problems plotting a Traverse wave, how would one ever plot a standing wave???