This is an interesting observation, thank you!

Well, of course the second answer is correct, the intensity is 4 times as big -- but where does the energy come from?

Think about where the energy of a single wave comes from. The moving charges, that produce the wave, are obviously doing work - against the force of the field coming from their own radiation.

(Wow, that's by the way a nice way one can see, that the intensity has to be quadratic in the frequency: the velocity is increased and the field is increased, so the power $F\cdot v$ is quadratic!)

So in this case the radiation fields will superpose, and every of the charges will do double work (same velocity against a double field) per period. There you have the energy.

In the usual system of distinct sources you can neglect the action of one on the other, so the net intensity is just (approximately, as I see now) the sum of the intensities of each source alone.

Very nice.

This is an interesting observation, thank you!

Well, of course the second answer is correct, the intensity is 4 times as big -- but where does the energy come from?

Think about where the energy of a single wave comes from. The moving charges, that produce the wave, are obviously doing work - against the force of the field coming from their own radiation.

(Wow, that's by the way a nice way one can see, that the intensity has to be quadratic in the frequency: the velocity is increased and the field is increased, so the power $F\cdot v$ is quadratic!)

So in this case the radiation fields will superpose, and every of the charges will do double work (same velocity against a double field) per period. There you have the energy.

In the usual system of distinct sources you can (to a certain approximation) neglect the action of one on the other, so the net energy production is just (approximately, as I see now) the sum of the energies produced by each of the sources alone.
This is consistent to the other, rather qualitative, reasoning: if you consider a shell around both sources, there will be some areas where the waves interfere positively (there you have 4 times the single intensity) and others where they interfere destructively and leave zero intensity, so when you take the mean you get approximately the double intensity of one source.

Very nice.

This is an interesting observation, thank you!

Well, of course the second answer is correct, but where does the energy come from?

Think about where the energy of a single wave comes from. The moving charges, that produce the wave, are obviously doing work - against the force of the field coming from their own radiation.

(Wow, that's by the way a nice way one can see, that the intensity has to be quadratic in the frequency: the velocity is increased and the field is increased, so the power goes quadratic!)

So in this case the radiation fields will superpose, and every of the charges will do double work. There you have the energy.

In the usual system of distinct sources you can neglect the action of one on the other, so the net intensity is just (approximately, as I see now) the sum of the intensities of each source alone.

This is an interesting observation, thank you!

Well, of course the second answer is correct, the intensity is 4 times as big -- but where does the energy come from?

Think about where the energy of a single wave comes from. The moving charges, that produce the wave, are obviously doing work - against the force of the field coming from their own radiation.

(Wow, that's by the way a nice way one can see, that the intensity has to be quadratic in the frequency: the velocity is increased and the field is increased, so the power $F\cdot v$ is quadratic!)

So in this case the radiation fields will superpose, and every of the charges will do double work (same velocity against a double field) per period. There you have the energy.

In the usual system of distinct sources you can neglect the action of one on the other, so the net intensity is just (approximately, as I see now) the sum of the intensities of each source alone.

Very nice.