# I Intensity of EM wave independent of frequency?

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1. Nov 27, 2016

### greypilgrim

Hi.

I'm a bit puzzled that the classical formula for the intensity of a monochromatic, linear EM wave
$$I=\frac{1}{2}\cdot c\cdot \varepsilon_0\cdot E_0 ^2$$
seems to be independent of frequency whereas I find for the energy of a mechanical wave (e.g. on a string with total mass $M$)
$$E=2\pi^2\cdot f^2\cdot A^2\cdot M\enspace .$$

Am I comparing apples and oranges or is it true that the energy transmitted per second per unit area only depends on the amplitude of the electric field?

2. Nov 27, 2016

### FactChecker

The intensity of a wave is usually per period of the wave, so it is very dependent on frequency.

3. Nov 27, 2016

### greypilgrim

I get easily confused with all those radiometry units. What I meant is the energy a wave carries through a surface per unit area per unit time, or power per unit area. This seems to be "irradiance". But the formula seems to be exactly the same (if the wave propagates perpendicularly to the surface). Still, no frequency. Since this is per unit time it is normalized to one second, not to a period of the wave.

4. Nov 28, 2016

### davenn

really ?
so if I have a 10W transmitter on 144MHz and I increase the power to 20W, you are telling me the freq is going to change ?

5. Nov 28, 2016

### FactChecker

No. Why would you think that? It is just how the term "intensity" is defined for a wave. https://en.wikipedia.org/wiki/Intensity_(physics)
You should draw appropriate logical conclusions about the relation between a wave's "intensity", frequency, and power.

6. Nov 29, 2016

### davenn

because it is what you stated

yet your link prefers a non freq dependence what is opposite to what you said

7. Nov 29, 2016

### FactChecker

I see your point. If something is measured on a per-unit basis, perhaps it should not be called dependent on the unit of measurement. But a change of units (like 1 cycle at two different frequencies) definitely changes things. That is what I meant. The frequency definitely has to be considered and has an effect. I think that is what the OP was expecting.

Last edited: Nov 29, 2016
8. Nov 29, 2016

### davenn

Unless some one can show me specifics, I would have to disagree with that
Again, using a larger step, transmit 10W step up to 100W the freq isn't going to change
if it did, it would make a lot of systems used today useless, but we know that doesn't happen

Now, if I do that power level increase as I stated, the intensity is going to change. There IS going to be a higher intensity ( W/m2 ) but it has nothing to do with the frequency being used.

Note the last sentence in the quote ... "in which case the average power transfer over one period of the wave is used"
The period/cycle is whatever you choose, there is no freq dependence.

To follow on from that. just as an aside .....
commercial transceivers use frequency control, not because they can change in power level and need to stop the frequency changing with different power levels. Frequency control is used to ensure the transmitter and receiver oscillators conform to their licenced frequency allocations.
So that the say, TV station technician can say the transmitter in transmitting on this freq (channel allocation) with this amount of bandwidth.

That is why free running oscillators are not used ... aging components, changing temperatures and other issues all conspire to cause undesirable changes in frequency ( frequency drift) ( regardless of the transmitter power)

Dave

Last edited: Nov 29, 2016
9. Nov 29, 2016

### FactChecker

There is no reason to say it would. Given a common definition of the term "intensity" for a wave, which is per cycle, one will have to use the correct corresponding relationships between intensity, power, and frequency. There are other definitions of the term "intensity" which are apparently not what was being used in the OP. In any case, changing intensity does not automatically force a frequency change.

Last edited: Nov 29, 2016