Confused about wavelength (basic)

[mishima]

I'm confused about how to think about wavelength for something physical, like a simple pendulum or harmonic oscillator. I understand graphically what wavelength is but can't seem to come up with a physical description. I was thinking about ocean waves and that wavelength could be the direct measurement crest to crest. But when I move that model to pendulums, oscillators, EM waves I get confused. Part of the confusion for me is that graphs of a wave for a harmonic oscillator, for example, are position on the y-axis and time on the x axis, and wavelength is measured along the x-axis. I know mathematically how period and wavelength are related but just need a more physical description of wavelength please. Is it just a pure number defined as product velocityXperiod with no real correlation to anything in the case of pendulum/SHO/EM? Or could it be the total distance, NOT displacement, traveled by a particle in one oscillation?

 

[bp_psy]

There is no such thing as the wavelength of an oscillator.The position vs time graph only shows you the position of the oscillator in time it does not describe a wave. Only waves have wavelength, it represents the distance between two points in the wave separated by a time period . Each point in a wave can be considered an oscillator and its position time graph is a sinusoid.

 

[billiards]

The wavelength is a property of a waveform, a famous example of a waveform being a sinusoid. As I am sure you are aware, it is simply the distance from crest to crest.

Waveforms can exist in time, as in the pendulum example; and waveforms can exist in space as in a snapshot of the ocean.

The wavelength of a pendulum is simply the time it takes to complete one oscillation.

 

[sjb-2812]

The wavelength of a pendulum is simply the time it takes to complete one oscillation.

Eh? How do you define frequency then?

 

[cjl]

The wavelength of a pendulum is simply the time it takes to complete one oscillation.

No, that's the period.

 

[billiards]

No, that's the period.

Yes you're right.

But it is very similar to the wavelength. Physically the period is analogous to the wavelength. The difference is only in the space that you measure them.

Of course if you're dealing with waves you need to consider time and space and so we distinguish wavelength from period. The wavelength is the length as measured from crest to crest, and the period is the time it takes for one oscillation to take place as measured at a point in space.

The pendulum is not really a wave. If you think of it as existing at a single point in space, then oscillations are purely in time. There is no wave passing through to cause this motion, it is purely an oscillation about a stable state. Thus it has a period and no proper wavelength. That's the best way to look at it.

But if you look at the waveforms in time alone, it is safe to abuse the convention and to refer to the period as the wavelength. I am a seismologist, and often I speak with colleagues of the "wavelength" of a signal on a time series -- of course the units of this "wavelength" are in time, so really it is not a waveLENGTH, however this does not bother us because the time series is purely a temporal measurement and there is no way that the meaning can be confused.

 

[billiards]

Eh? How do you define frequency then?

Frequency is the number of oscillations per unit time.

If one oscillation takes P seconds. Then there are 1/P oscialltions per second. F = 1/P.




As an aside, what is the analogue of frequency in space? That would be the number of full waveforms per unit length.

So if the is one wavecycle every L metres. Then there are 1/L waves per metre. k=1/L.

We call this property, k the wavenumber.

 

[mishima]

Thanks billiards, that was most excellent.