# What exactly is a wavelength?

syano
Hi, I am new to this site, and it certainly looks very interesting! I'm new to physics too.

I have a queastion that will surly be elementry to the topics I have seen on this forum so far... but what they hey... I'm a newb.

When I read articals about the electromagnetic spectrum, they refer to the word "wavelength" a lot. When I look up this term is says a wavelength is the distant between adajacent peeks in a wave.

This makes sense to me in if all waves are perfectly symetrical. Like the drawing below (hope it looks right from your view)
_ _
\_/ \_/ \_/

But it doesn't make sense if light waves can travel asymetrical like the drawing below.
_ _
/ \_ _ _ / \
\_/ \__/ \_/ \_/ \

Perhaps all light wave travel with symetrical waves? Or perhaps I'm totaly missing something.

Thanks,

Syano

syano
bah. The drawings came out all wrong when I posted. I'll try and post a pic if my question is unclear.

Thanks again,

S

A single color wave is usually treated as a sine curve. Peak to peak is well-defined.

syano
Thanks for the response Mathman.

Again, sorry about those drawings. I found some pics on the internet to explaine myself better.

A nice smooth wave looks like this to me. http://www1.law.ucla.edu/~kang/commlaw/assets/images/autogen/a_1-3analogwave.gif [Broken]

And a scribbled wave looks like this to me. http://www.sfu.ca/sonic-studio/handbook/Graphics/Cycle1.gif

I understand how you can measure the wavelength of a smooth wave (like the fist pic) by measuring the distance from crest to crest, or trough to trough, or from one point on that wave to the next point where the wave begins to repeat itself.

But I do not understand how you could measure the wavelength of a scribbled wave (like the second pic) by measure from crest to crest, or trough to trough... However I understand how you could measure this by the distance of one point on the wave to the next point where the wave begins to repeat itself.

Are all EM waves, nice and smooth like the first pic? And if they are not, would it be inaccurate to measure the wavelength of a scribbled wave by measuring from crest to crest, or trough to trough?

Thanks,

Syano

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Staff Emeritus
Gold Member
Both the smooth curve and the "scribbled" curve have defined wavelengths, because they repeat indefinitely. The smallest unit of repitition is called the "fundamental" wavelength.

For a pure sine wave, there is only one (obvious) way to define wavelength. The repetitive unit is a single sine cycle.

For a complex (yet periodic) wave, the same concept of wavelength still applies: the overall wavelength is the width of the smallest repeating unit.

Think about a complex wave formed by the addition of two sine waves, one twice the wavelength of the other. Draw a picture of it if you want, or graph it on a graphic calculator:

y = sin(x) + sin(2x)

You know what this wave is made of: one sine wave of one frequency, and another of double frequency. One of one wavelength, and another of half that.

Look on your graph: the smallest repetitive unit is 2 pi radians in wavelength, the wavelength of the lowest-frequency component: sin(x).

This is an example of the general rule:

For a complex signal -- one that is made as a sum of independent sine waves -- the overall wavelength is always the wavelength of the lowest-frequency (longest-wavelength) component. The lowest-frequency (longest-wavelength) component is called the "fundamental."

Now, as it turns out, Fourier demonstrated that ANY complex, periodic signal can be made out of a (perhaps infinite) number of independent sine waves -- so the above bold-face rule applies to ANY complex signal.

All this stuff is pretty neat-o: you can take any periodic signal, no matter how complex, and perform what's called a "Fourier transform" on it. What you get is a chart of all the frequencies contained in the signal -- the amplitudes and phases of all the sine waves you could add together to recreate it.

The most obvious application of this is in musical instruments. You know that even when a clarinet and a trumpet play the same note, say middle C, you somehow know which instrument is which. You may also know that no instrument really plays exactly one frequency -- if it did, it would be boring! Instead, all instruments play harmonics -- frequencies that are a multiple of 2, 3, 4, etc. of the fundamental note, middle C. The fundamental note is by far the dominant note, but the higher harmonics serve to color the sound and make a clarinet sound distinctly different from a trumpet.

Does this make sense?

- Warren

Mr. Robin Parsons
Nice explanation Warren, (oooops Chroot) YUP! it makes sense to me.

StephenPrivitera
Do we say that a wave is treated as a sine wave because of the way waves interfere? I don't quite understand what the structure of a wave looks like. There are no physical "peaks" right? We draw a wave like a sine curve, but it doesn't really look like anything. How does the idea of photons affect this sine wave representation?

Staff Emeritus
Gold Member
Originally posted by StephenPrivitera
Do we say that a wave is treated as a sine wave because of the way waves interfere? I don't quite understand what the structure of a wave looks like. There are no physical "peaks" right? We draw a wave like a sine curve, but it doesn't really look like anything. How does the idea of photons affect this sine wave representation?
What do you mean... the structure of a wave? What's a "physical peak?" The sine wave is a mathematical object. Surely you are familiar with real waves, e.g. sound waves and water waves.

- Warren

StephenPrivitera
Ok, I guess I'm thinking mostly of EM waves. I mean to say that we use the sine wave to represent EM waves because these waves interfere in the same way that sine waves sum, as in your example. In an EM wave, there's no physical crest or trough as in water waves, right? Does it make sense to say that an EM wave looks like a sine wave? Or is it better to say that it behaves like a sine wave?

Staff Emeritus