- #1

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He defined K=2π/λ and k=1/λ and both of them have the same units (i.e, meter inverse)

What does wave number of a Harmonic function tells about?

- Thread starter manimaran1605
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- #1

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He defined K=2π/λ and k=1/λ and both of them have the same units (i.e, meter inverse)

What does wave number of a Harmonic function tells about?

- #2

olivermsun

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K=2π/λ is in units of radians/m and k=1/λ has units cycles/m, where "radians" and "cycles" are usually omitted. You just have to remember which kind of units you're using, so you know whether there needs to be a factor of 2π inside the sine/cosine/exponential.

For example, a wave of "propagation number(K)" would be sin(Kx), while a wave with "wave number(k)" would be sin(2πkx).

- #3

jtbell

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You have it backwards. He defines the propagation number as ##k = 2 \pi / \lambda## (lower-case Latin letter "k") and the wave number as ##\kappa = 1 / \lambda## (lower-case Greek letter "kappa", not upper-case Latin letter "K"). Those different symbols (##k##, ##\kappa##, and ##K## in LaTeX; or k, κ, and K in PF's default font) tend to confuse people. Look carefully![Hecht] defined [propagation number] K=2π/λ and [wave number] k=1/λ

As olivermsun noted, the units are different. ##k## is much more commonly used. ##\kappa## is mainly used by spectroscopists. I don't know if they have a practical reason for it, or if it's just a historical convention.

Last edited:

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olivermsun

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That way, you can write things like ##e^{i(kx - \omega t)}## without having ##2\pi##s all over the place.

- #5

jtbell

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Exactly. The OP (manimaran1605) should compare equation (2.24) in Hecht with the other equations in that group on page 16, which are different ways of writing the same wave equation using different combinations of constants.That way, you can write things like ##e^{i(kx - \omega t)}## without having ##2\pi##s all over the place.

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