# Is energy of a wave based solely on its frequency? And for matter?

1. Aug 23, 2014

### shangriphysics

Is energy of the wave solely based on frequency?

I know E=hf.

Is energy of matter based on E=mc^2?

2. Aug 23, 2014

### Staff: Mentor

What do you mean with "based on", and which type of waves?
The energy of individual photons just depends on their frequency, with E=hf.

This should be written as $E_0=mc^2$ (energy at rest is ...) or $E=\gamma mc^2$, as the energy depends on the mass and the velocity (hidden in the Lorentz factor $\gamma$).

3. Aug 23, 2014

### shangriphysics

Ahh, I meant, is the energy of a sound wave, light wave, rope wave, related to frequency?

Thank you Mfb!

4. Aug 24, 2014

### Staff: Mentor

Well, for classical waves you always have to consider the intensity/amplitude/related values.

5. Aug 24, 2014

### shangriphysics

I thought that the amplitude was related to the energy I put into the wave? Is there a difference between the energy I put into the wave, and the energy the wave has or can emit(transmit)?

Lastly, you mentioned that energy of photons are dependent on the frequency, but what about energy for sound waves and rope waves. I know that a photon is a wave too.

I am not sure, but I am thinking that the energy of a sound wave is related to intensity, frequency, and amplitud, a light wave is related to frequency and amplitude, and the energy of the rope wave will be dependent on frequency and amplitude?

Thanks for taking the time to help me MFB!

Last edited: Aug 24, 2014
6. Aug 24, 2014

### Staff: Mentor

Those are all problematic concepts. To have a fixed energy, you cannot consider a continuous wave, you have to make wave packets - this just leads to more confusion, so let's avoid that.

It is probably better to consider waves in terms of power (energy per time): if you can neglect losses in the transmission, then transmitted power is always equal to the input power, this is just given by energy conservation.

It is not useful to ask if energy or power in waves depend on the frequency. There is no relevant relationship in between.

7. Aug 24, 2014

### shangriphysics

Ahh, I get this interms of power and conservation!

I promise this is my last question for this forum!
I was asking these questions because on one of khan academy or doc physics videos(I don't remember), they said that the second harmonic has more Energy than the first harmonic. I thought it had something to do with frequency. How can we say that the second harmonic has more energy than the first harmonic? Is it an erroneous claim?

8. Aug 24, 2014

### Staff: Mentor

A complex signal (e.g. a sound) can be expressed as a sum of "pure" sinusoidal waves, each with a different frequency and amplitude. For more details, look up "Fourier analysis." Each of these waves has energy proportional to the square of its amplitude.

9. Aug 24, 2014

### shangriphysics

Thanks Jtbell!

10. Aug 24, 2014

### Staff: Mentor

I certainly hope not!

The energy of a wave is proportional to the square of the frequency and also proportional to the square of the amplitude:

http://hyperphysics.phy-astr.gsu.edu/hbase/waves/powstr.html

So a second harmonic of equal amplitude would indeed have more energy. However, in most real signals the second harmonic probably does not have equal amplitude, so the statement is not generally true.

11. Aug 24, 2014

### shangriphysics

Hi DaleSpam,

I was wondering if that equation can related to all types of waves, for example, light, rope, and sound?
In the link it says for a string.

Maybe light is related to the equation E=hf, and sound is related to intensity, and string/rope is related to the link you provided?

You made me counter my last question statement haha. I meant last question for this forum page, but not physicsforums! Oo never! I love this site too much, and I have so many questions on physics!

12. Aug 24, 2014

### Staff: Mentor

In classical electrodynamics, light consists of waves of electric and magnetic fields. The energy carried by the wave is proportional to the square of the amplitude (maximum value) of the fields.

In quantum electrodynamics, light consists of photons. A single photon has energy E=hf. The light coming out of your desk lamp contains bazillions of photons. In this case you can relate the number of photons to the (classical) amplitude of the electric and magnetic fields in the wave, by way of the total energy in the wave.

If the light is so weak that it contains only a few photons, it's not meaningful to talk about classical electric and magnetic fields any more, and you have to use quantum electrodynamics.