Pi/2 Translational Difference in y(x,t) Equations

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Homework Help Overview

The discussion revolves around the equations for wave motion, specifically comparing the cosine and sine forms of the wave equation, y(x,t)=Acos(kx-ωt) and y(x,t)=Asin(kx-ωt). Participants are exploring the implications of a translational difference of π/2 between these two representations.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the significance of initial conditions in wave equations and whether the choice between sine and cosine affects the results. Some raise questions about the implications of the translational difference and its relation to wave motion.

Discussion Status

There is an ongoing exploration of the relationship between the two forms of the wave equation. Some participants suggest that both forms can yield similar results under certain conditions, while others clarify the nature of the translational difference and its impact on interpretation.

Contextual Notes

Participants mention the theoretical context of sound waves and the relevance of initial conditions, indicating that the choice of equation may depend on specific scenarios or calculations.

Helicobacter
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In my text
y(x,t)=Acos(kx-ω t)
In the teacher's handout:
y(x,t)=Asin(kx-ω t)
There's a translational difference of pi/2 between them! I don't know which one to use for the test :S
 
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hehe, its just a matter of initial condition (with difference of pi)
and thereotically an ideal sound wave is usually calculated for a stablized value which means the initial condition doesn't matter much.. very seldom do we need to know its initial condition..
so no matter sin or cos will end up with e same results.
and u can use either one u want due to different kinds of calculations
 
To be accurate, there's a translational difference of pi/2k between them.

Or looking at it a different way, there is a time difference ot pi/2ω

As zergju says, they both represent "the same wave motion", but measured relative to differet points in space and/or time.
 
That was helpful, thanks
 

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