amplitude, intensity, energy

[AA|FCB|DOC]

Does anyone know how the amplitude, intensity, and energy of a wave are mathematically related? I know as one increases all the other ones do too, but does anyone have a specific formula that they know. Or a proportional relationship? Thanks in advance

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[brood910]

Does anyone know how the amplitude, intensity, and energy of a wave are mathematically related? I know as one increases all the other ones do too, but does anyone have a specific formula that they know. Or a proportional relationship? Thanks in advance

As far as I know, there's no formula for them.

 

[milski]

The energy is proportional to the amplitude squared. Intensity, by definition, is just the average power (or energy/over time) per unit area.

The formulas are slightly different for transverse and longitudinal waves, since the setups are slightly different. For transverse, you usually talk about energy distributed over a length and that's E=0.5μω^2.A^2.L. For longitudinal waves (in 3D), you'd talk about energy per volume and you have Ε=0.5ρω^2.s0^2.V.

 

[Francium87]

For Longitudinal wave

Intensity is dependent on the source of the wave and the medium it travels through

Angular frequency (w) and Amplitude (A) depend on the source of wave ;
Velocity (v) and density (p) depend on the medium

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therefore Intensity (I) = 1/2 p w^2 A^2 v

 

[MedGrl@2022]

The energy is proportional to the amplitude squared. Intensity, by definition, is just the average power (or energy/over time) per unit area.

The formulas are slightly different for transverse and longitudinal waves, since the setups are slightly different. For transverse, you usually talk about energy distributed over a length and that's E=0.5μω^2.A^2.L. For longitudinal waves (in 3D), you'd talk about energy per volume and you have Ε=0.5ρω^2.s0^2.V.

The equation that you gave for the transverse wave. Does that equation hold true for light and electromagnetic waves or only other types of transverse waves?

 

[milski]

The equation that you gave for the transverse wave. Does that equation hold true for light and electromagnetic waves or only other types of transverse waves?

It does but some details like what is μ in that case and what is an amplitude need to be discussed. It's not something that you should worry about for the MCAT.

 

[sazerac]

With light isn't E only related to frequency and nothing else?

 

[milski]

With light isn't E only related to frequency and nothing else?

E as in energy or E as in electric field?

For a single photon, yes, the energy is related only to the frequency. For a lot of practical situations (radio transmitters, microwave ovens, light sources, etc.) you're not going to talk in terms of number of photons but in terms of magnitude of the E/B fields. In these cases, the energy can be expressed as a function of the magnitude of the electric/magnetic field.

 

[AA|FCB|DOC]

hmmm thanks for the clarification. I think for the MCAT knowing that energy is directly proportional to Amplitude squared should be enough, right?

 

[milski]

hmmm thanks for the clarification. I think for the MCAT knowing that energy is directly proportional to Amplitude squared should be enough, right?

I would think so but I don't write the questions. 😉