Two sources of equal amplitude undergo interference the energy at maxima is four times that due to either source is this a violation of the principle of conservation of energy. Explain.
Can someone help me summarize a good model answer and further explanation of the answer? Thanks :)
The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed from one form to another. In the case of interference, the energy remains conserved as long as the energy at the maxima is four times that due to either source.
Let's break down the model answer and further explanation:
1. Interference: Interference occurs when two waves overlap in space and time. In this case, we have two sources of equal amplitude, meaning they are producing waves of the same intensity or strength.
2. Energy at the maxima: When the two waves interfere constructively (in-phase), the amplitude of the resultant wave is the sum of the amplitudes of the two interfering waves. Since the sources have equal amplitude, the resultant wave at the maxima will have double the amplitude compared to a single source.
3. Energy calculation: The energy of a wave is proportional to the square of its amplitude. Therefore, the energy at the maxima of the resultant wave will be four times that of either individual source because (2*amplitude)^2 = 4*(amplitude)^2.
4. Conservation of energy: Even though the energy at the maxima is four times that of either source, the total energy in the system remains conserved. The extra energy at the maxima is obtained by redistributing the energy from other points where destructive interference occurs. Hence, there is no violation of the principle of conservation of energy.
In conclusion, the question doesn't violate the principle of conservation of energy because even though the energy at the maxima is four times that of either source, the energy redistribution from other points ensures that the total energy in the system remains conserved.