Optics: Determine which of the following describe traveling waves

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SUMMARY

This discussion focuses on the characteristics of traveling waves and the validity of wave equations. A valid wave equation must take the form f(ax-bt), where linear terms are essential. The participants analyze specific equations, determining that equation (d) is valid while discussing the implications of squared terms in equations (a), (b), and (c). The direction of travel for the wave represented by az² - bt² is also questioned, highlighting the importance of understanding wave directionality.

PREREQUISITES
  • Understanding of wave equations and their forms
  • Familiarity with linear terms in mathematical functions
  • Knowledge of wave directionality and its implications
  • Basic grasp of trigonometric functions, specifically cosine
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  • Learn about the implications of non-linear terms in wave equations
  • Study the concept of wave directionality in physics
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Students and educators in physics, mathematicians studying wave mechanics, and anyone interested in the mathematical foundations of traveling waves.

Shackleford
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I'm really rusty on waves. What characteristics am I looking for? With respect to its variables, doesn't a valid wave equation have to contain only linear terms in its argument(s)?

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Shackleford said:
I'm really rusty on waves. What characteristics am I looking for? With respect to its variables, doesn't a valid wave equation have to contain only linear terms in its argument(s)?

Yes, a wave has the form f(ax-bt).

ehild
 
ehild said:
Yes, a wave has the form f(ax-bt).

ehild

Yes, I know that.

It appears (d) is valid, but what about (a), (b), and (c)? I guess I'm not sure what the squares do. Of course, I recognize the form of the equation without the squares.
 
Last edited:
Having (ax±bt)2 shouldn't matter. The squaring can be considered to be part of function, f .
 
SammyS said:
Having (ax±bt)2 shouldn't matter. The squaring can be considered to be part of function, f .

Same goes for cos2, too?
 
Shackleford said:
Same goes for cos2, too?
Yes.
 
What about (b)? It has az2 - bt2.
 
If it is a traveling wave, in what direction does it travel? +z or -z?

ehild
 

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