What is the relationship between intensity and amplitude in a wave source?

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SUMMARY

The intensity of a wave is directly proportional to the square of its amplitude, as established in wave theory. When five identical wave sources with amplitude A0 are superimposed, their collective amplitude becomes 5A0, resulting in an energy increase by a factor of 25 only if they are perfectly in phase. If the sources oscillate out of phase, the total energy radiated increases only by a factor of 5. This relationship highlights the critical role of phase alignment in determining the overall intensity of wave sources.

PREREQUISITES
  • Understanding of wave mechanics and properties
  • Knowledge of amplitude and intensity relationships
  • Familiarity with oscillatory motion and energy concepts
  • Basic principles of superposition in wave theory
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  • Study the mathematical derivation of intensity and amplitude relationships in wave physics
  • Explore the effects of phase differences on wave interference patterns
  • Investigate the power radiated by oscillating charges in electromagnetic theory
  • Learn about superposition principles in different wave contexts, such as sound and light
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Students and professionals in physics, particularly those studying wave mechanics, acoustics, and electromagnetic theory, will benefit from this discussion.

Gauss M.D.
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This is something I don't relly get. I keep reading that the intensity of a wave is proportional to the square of its amplitude.

So let's suppose we have a random wave source, with amplitude A0. If we replace that source with five identical copies of it, their collective amplitude is 5A, yes? But have I really raised the energy level at the source by a factor of 25? What am I missing here?
 
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Gauss M.D. said:
If we replace that source with five identical copies of it, their collective amplitude is 5A, yes? But have I really raised the energy level at the source by a factor of 25? What am I missing here?

Are you assuming that the 5 identical sources are located in exactly the same spot (superimposed on one another)? If so, then I believe the total energy radiated by the sources would be 25 times greater than one source alone.

Think about the special case where the source is just a single charge q oscillating in simple harmonic motion . Superimposing 5 such oscillators is simply equivalent to increasing the charge from q to 5q. The power radiated by an oscillating charge is proportional to the square of the charge. So, the energy radiated with 5q is 25 times that of q.

If the 5 oscillators do not oscillate in phase, but have randomly changing phase shifts relative to one another, then I believe the average radiated power output would be just 5 times that of one oscillator.
 
How do intensity, amplitude, and power all relate to each other in this context?
 

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