So I have a small question for the POV-Ray memetic search engine: How 
much energy does a wave have?

I actually can't figure this one out. Presumably the energy of a wave is 
a function of its amplitude, but I have a feeling frequency is involved 
as well. (But I'm not sure in which polarity.)

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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Am 07.05.2010 20:25, schrieb Orchid XP v8:
> So I have a small question for the POV-Ray memetic search engine: How
> much energy does a wave have?
>
> I actually can't figure this one out. Presumably the energy of a wave is
> a function of its amplitude, but I have a feeling frequency is involved
> as well. (But I'm not sure in which polarity.)

As the potential gradients are higher, I'd guess high-frequency waves 
have a higher energy (given a fixed amplitude) - just like with EM waves.

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> So I have a small question for the POV-Ray memetic search engine: How much 
> energy does a wave have?

What sort of wave?

> I actually can't figure this one out. Presumably the energy of a wave is a 
> function of its amplitude, but I have a feeling frequency is involved as 
> well. (But I'm not sure in which polarity.)

The energy of a photon is easy to look up, and depends only on the 
wavelength (lower wavelength = more energy).  Obviously then you can figure 
out how many photons are required for a certain power level, and then how 
much time is needed to transfer a given amount of energy.

In electric circuits you can figure out instantaneous power flow by using 
P=IV.  Then you can integrate this power over time to get energy.  For 
example a sine wave has a known result, because it is so common in AC 
circuits, that is where RMS voltage/current comes from.

For water waves, I would imagine you need to look at the potential energy of 
the water as it moves up and down, look up Wave Energy on wikipedia - it has 
some formulas and example calculations.

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scott <sco### [at] scottcom> wrote:
> The energy of a photon is easy to look up, and depends only on the 
> wavelength (lower wavelength = more energy).

  Are you sure the energy does not depend on amplitude? One would think
that you need more energy for a larger amplitude.

-- 
                                                          - Warp

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scott wrote:
>> So I have a small question for the POV-Ray memetic search engine: How 
>> much energy does a wave have?
> 
> What sort of wave?

Does it make a difference? I thought the properties of waves were fairly 
universal.

> The energy of a photon is easy to look up, and depends only on the 
> wavelength (lower wavelength = more energy).

Or, to put it another way, higher frequency = more energy.

> For water waves, I would imagine you need to look at the potential 
> energy of the water as it moves up and down, look up Wave Energy on 
> wikipedia - it has some formulas and example calculations.

Sound waves are what really interest me, but presumably water waves 
being mechanical have similar properties...

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On Mon, 10 May 2010 13:03:54 +0200, Warp <war### [at] tagpovrayorg> wrote:
> scott <sco### [at] scottcom> wrote:
>> The energy of a photon is easy to look up, and depends only on the
>> wavelength (lower wavelength = more energy).
>
>   Are you sure the energy does not depend on amplitude? One would think
> that you need more energy for a larger amplitude.

In the case of photons, the "amplitude" of the "wave" is just a measure of  
how many photons there are. The energy of an individual photon depends  
only on its wavelength/frequency.



-- 
FE

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>> The energy of a photon is easy to look up, and depends only on the
>> wavelength (lower wavelength = more energy).
>
>  Are you sure the energy does not depend on amplitude?

Yes, the formula for energy of a photon only has one variable, wavelength.

> One would think
> that you need more energy for a larger amplitude.

You do, but that's just because you have more photons, not because each 
photon has more energy.

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> Sound waves are what really interest me, but presumably water waves being 
> mechanical have similar properties...

I guess in water there are really two types of "wave".  The huge waves that 
you see on the surface and crashing against the coast moving in 2D are one 
type, but the other type is disturbances under the surface that are 
transmitted as pressure waves in 3D.  Those are probably more similar to 
sound waves.

Wikipedia has several pages about sound and pressure/power:

http://en.wikipedia.org/wiki/Sound
http://en.wikipedia.org/wiki/Sound_power

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4be7e95f@news.povray.org...
>
> Sound waves are what really interest me, but presumably water waves being 
> mechanical have similar properties...
A big difference is that water waves propagation speed depends on wavelength
http://www.exo.net/~pauld/activities/waves/waterwavespeed.html

Marc

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scott wrote:
>> Sound waves are what really interest me, but presumably water waves 
>> being mechanical have similar properties...
> 
> I guess in water there are really two types of "wave".  The huge waves 
> that you see on the surface and crashing against the coast moving in 2D 
> are one type, but the other type is disturbances under the surface that 
> are transmitted as pressure waves in 3D.  Those are probably more 
> similar to sound waves.

Waves only "crash" near to the shore, due to the solid seabed 
interrupting the wave cycle. (Apparently.) Waves on the surface of a 
"deep" (WRT wavelength) body of water do not exhibit this effect.

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