Help Defining a Wave

[Viper0329]

I'm currently working on a metaphysics paper dealing with the nature of waves. Specifically, I'm writing about the Wave Structure of Matter, which posits that all things (including particles) in the universe are ultimately composed of waves moving in a medium (space).

Before I do anything, I need to define what exactly a wave is. Is a wave simply a disturbance in a medium? Is it defined as the mathematical relation between a trough and a crest? Basically, what I need to understand is the nature of a wave. Thomistically, is it a real being (a substance which exists on its own) or a mental being (an abstraction)? I'm leaning towards an abstraction since a wave must exist in a medium. Any thoughts?

 

[djhuber82]

I would say that the defining characteristic of a wave is it's periodicity. A wave is some phenomenom we identify that, as you said, exists in a medium, and posesses a measurable quantity that is periodic or quasi-periodic in either space or time or both. Something that has nonzero frequency.

 

[smack Down]

Originally posted by: djhuber82
I would say that the defining characteristic of a wave is it's periodicity. A wave is some phenomenom we identify that, as you said, exists in a medium, and posesses a measurable quantity that is periodic or quasi-periodic in either space or time or both. Something that has nonzero frequency.

Waves need not be periodic for example when two sin waves are (multipled?) together and there ratio of frequency is irrational the output is not periodic for example sqrt(2) and 1

 

[itachi]

Originally posted by: smack Down
Waves need not be periodic for example when two sin waves are (multipled?) together and there ratio of frequency is irrational the output is not periodic for example sqrt(2) and 1

that's still periodic. the sine product can be seperated into a sum of cosine components with individual frequencies.
i.e.,
y = sin a * sin b = 0.5*(e^ia - e^-ia) * 0.5*(e^ib - e^-ib)
y = 0.25 * (e^i(a + b) - e^i(a-b) - e^-i(a - b) + e^-i(a + b))
y = 0.25 * (e^i(a + b) + e^-i(a + b)) - 0.25 * (e^i(a - b) + e^-i(a - b))
y = 0.5cos(a + b) - 0.5cos(a - b)
now it's not described as a single wave.. but as the superposition of two waves.

Before I do anything, I need to define what exactly a wave is. Is a wave simply a disturbance in a medium? Is it defined as the mathematical relation between a trough and a crest? Basically, what I need to understand is the nature of a wave. Thomistically, is it a real being (a substance which exists on its own) or a mental being (an abstraction)? I'm leaning towards an abstraction since a wave must exist in a medium. Any thoughts?

i don't think a wave is really an entity of it's own. i'd say that a wave is the periodic sinusoidal oscillation of a group of particles in space and time, produced by the absorption of energy by the particles.

 

[DrPizza]

I wouldn't use the term "medium", as electromagnetic waves do not need a medium to propagate through. Initially, it was proposed that they *did* require a medium, and the medium was termed the ether. Simple experiments, IIRC, based on the earth's changing direction (180 days apart in its orbit) showed that this ether did not exist.

edit: wow, I'm having trouble with thinking up a good definition of a wave. Could the definition state something about transferring energy, ie a wave is the transfer of energy from one location to another location?

 

[smack Down]

Originally posted by: itachi

Originally posted by: smack Down
Waves need not be periodic for example when two sin waves are (multipled?) together and there ratio of frequency is irrational the output is not periodic for example sqrt(2) and 1

that's still periodic. the sine product can be seperated into a sum of cosine components with individual frequencies.
i.e.,
y = sin a * sin b = 0.5*(e^ia - e^-ia) * 0.5*(e^ib - e^-ib)
y = 0.25 * (e^i(a + b) - e^i(a-b) - e^-i(a - b) + e^-i(a + b))
y = 0.25 * (e^i(a + b) + e^-i(a + b)) - 0.25 * (e^i(a - b) + e^-i(a - b))
y = 0.5cos(a + b) - 0.5cos(a - b)
now it's not described as a single wave.. but as the superposition of two waves.

Right but the wave that occurs in the real world is not periodic. Have the requiriment that a wave be periodic will limit what you can do with a wave because if you add two waves together you can get not a wave.

 

[itachi]

Originally posted by: smack Down
Right but the wave that occurs in the real world is not periodic. Have the requiriment that a wave be periodic will limit what you can do with a wave because if you add two waves together you can get not a wave.

what waves are you talking about? if the source of energy is constant, a wave will be periodic.. when it's superposed with another wave, you get a combination of waves. even though that may not be a wave, it can be represented as a linear combination of waves. the fact that waves are periodic allows frequency to be associated with them, where f = 1 / T.

edit: wow, I'm having trouble with thinking up a good definition of a wave. Could the definition state something about transferring energy, ie a wave is the transfer of energy from one location to another location?

yea.. i know what u mean. i think the definition would have to include the transfer of energy.. while i was trying to think up a definition, the main characteristic that i noticed was that they form when energy is applied to a particle.

 

[xtknight]

This sounds like what you're looking for in terms of a definition? I'm far from any physical scientist but it sounded good to me.

http://www.nmlites.org/standards/science/glossary_6.htm

 

[silverpig]

d^2 Psi / dxi^2 = d^2 Psi / dt^2

 

[smack Down]

Originally posted by: itachi

Originally posted by: smack Down
Right but the wave that occurs in the real world is not periodic. Have the requiriment that a wave be periodic will limit what you can do with a wave because if you add two waves together you can get not a wave.

what waves are you talking about? if the source of energy is constant, a wave will be periodic.. when it's superposed with another wave, you get a combination of waves. even though that may not be a wave, it can be represented as a linear combination of waves. the fact that waves are periodic allows frequency to be associated with them, where f = 1 / T.

sin(2*pi*sqrt(2))*sin(2*pi*2) is a wave but it is not periodic.

 

[TuxDave]

Originally posted by: smack Down

Originally posted by: itachi

Originally posted by: smack Down
Right but the wave that occurs in the real world is not periodic. Have the requiriment that a wave be periodic will limit what you can do with a wave because if you add two waves together you can get not a wave.

what waves are you talking about? if the source of energy is constant, a wave will be periodic.. when it's superposed with another wave, you get a combination of waves. even though that may not be a wave, it can be represented as a linear combination of waves. the fact that waves are periodic allows frequency to be associated with them, where f = 1 / T.

sin(2*pi*sqrt(2))*sin(2*pi*2) is a wave but it is not periodic.

It looks like a constant to me.

 

[Born2bwire]

Originally posted by: smack Down
sin(2*pi*sqrt(2))*sin(2*pi*2) is a wave but it is not periodic.

That would be a constant.

Itachi is correct. Waves are still considered to be periodic in nature due to the fact that they are a linear superposition of single frequency waves. Waves are described by the progression of a constant phase front that is periodic in space and time.

 

[smack Down]

Originally posted by: Born2bwire

Originally posted by: smack Down
sin(2*pi*sqrt(2)t)*sin(2*pi*2t) is a wave but it is not periodic.

That would be a constant.

Itachi is correct. Waves are still considered to be periodic in nature due to the fact that they are a linear superposition of single frequency waves. Waves are described by the progression of a constant phase front that is periodic in space and time.

sin(2*pi*sqrt(2)t)*sin(2*pi*2t)
Please DIAF you know all that was missing is a t and the point stands the wave is not periodic.

 

[CycloWizard]

A wave is defined by an amplitude, a frequency, and a phase. These three things can uniquely identify a wave, if memory serves. I would say it is a real being rather than an abstraction, as there are many, many physically observable forms of waves.

 

[brentkiosk]

Sillverpig's definition is pretty good. A wave is the solution to a wave equation (classical or quantum mechanical).

 

[itachi]

Originally posted by: smack Down
sin(2*pi*sqrt(2)t)*sin(2*pi*2t)
Please DIAF you know all that was missing is a t and the point stands the wave is not periodic.

of course it's not, what you got isn't simply 1 wave.. it's 2 waves superposed with one another.

using what i said above..
y = sin(2pi sqrt(2)t) * sin(2pi2t)
y = 0.5cos(2pi(sqrt(2)-2)t) - 0.5cos(2pi(sqrt(2)+2)t)
how is that not a superposition of 2 waves (graph it out if you need more proof)?

 

[Viper0329]

How would one define a scalar wave then?

Check this out to see what I'm working with

Yes, this guy needs a huge lesson in web design and how to write an academic work.

 

[hypn0tik]

Originally posted by: itachi

Originally posted by: smack Down
sin(2*pi*sqrt(2)t)*sin(2*pi*2t)
Please DIAF you know all that was missing is a t and the point stands the wave is not periodic.

of course it's not, what you got isn't simply 1 wave.. it's 2 waves superposed with one another.

using what i said above..
y = sin(2pi sqrt(2)t) * sin(2pi2t)
y = 0.5cos(2pi(sqrt(2)-2)t) - 0.5cos(2pi(sqrt(2)+2)t)
how is that not a superposition of 2 waves (graph it out if you need more proof)?

It may be a superposition of 2 waves, but it still isn't periodic. The definition of a periodic function is as follows:

x(t) = x(t + nT) for integer n and period T.

Try and find n and T in the example above. You'll see that there is no common period for the superposition of the two waves.

 

[itachi]

Originally posted by: hypn0tik
It may be a superposition of 2 waves, but it still isn't periodic. The definition of a periodic function is as follows:

x(t) = x(t + nT) for integer n and period T.

Try and find n and T in the example above. You'll see that there is no common period for the superposition of the two waves.

that's not what i was trying to say. my point was that what he claimed to be a wave was actually the superposition of two waves. i wasn't attempting to argue that a superposed wave is periodic, just that his example wasn't a single wave.

 

[TuxDave]

Originally posted by: smack Down

Originally posted by: Born2bwire

Originally posted by: smack Down
sin(2*pi*sqrt(2)t)*sin(2*pi*2t) is a wave but it is not periodic.

That would be a constant.

Itachi is correct. Waves are still considered to be periodic in nature due to the fact that they are a linear superposition of single frequency waves. Waves are described by the progression of a constant phase front that is periodic in space and time.

sin(2*pi*sqrt(2)t)*sin(2*pi*2t)
Please DIAF you know all that was missing is a t and the point stands the wave is not periodic.

Haha, in THAT case it's not periodic but you're cheating by using a wave with an irrational frequency.