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I have a question regarding waves and the equation we use to describe their motion. My understanding feels shaky, so i'd like to see if I can get a good explanation/way of thinking about it.

The displacement of a particle in a $+x$ moving wave is given by;

$y = A \sin(2 \pi ft - \frac{2\pi x}{\lambda})$

But when this is contrasted to a specific example, is it correct to equate parts of the equation to one another?

For example, if I have $y = 0.021\sin(25t - 2x)$ does this imply that $2\pi ft = 25t$ and $\frac{2\pi x}{\lambda} = 2x$

And you can solve for frequency and wavelength respectively?

I hope my question makes sense.

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Yes, it means just that. The prefactor of the trigonometric function describing the wave is given by the amplitude, the prefactors of time and position in the argument give you the periodicity/frequency and wavelength, respectively.

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  • $\begingroup$ Thanks for the answer. That's a great relief - My text book only briefly touches on the subject, but i've seen questions using these ideas come up on past exams. $\endgroup$ – jm22b Apr 22 '14 at 14:45

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