Understanding Intensity and Amplitude of Physical Waves | School Physics UK

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SUMMARY

The discussion centers on the relationship between intensity and amplitude in physical waves, emphasizing that the energy of a wave is proportional to the square of its amplitude. This principle is crucial in understanding wave behavior, particularly in sinusoidal systems where both kinetic and potential energies are considered. The mathematical representation of power, P = V x I, illustrates how energy calculations account for the squared terms to prevent cancellation of positive and negative values. This foundational concept is applicable across various physical systems, including vibrating springs and electrical circuits.

PREREQUISITES
  • Understanding of sinusoidal functions and their properties
  • Basic knowledge of electrical circuits, specifically voltage and current relationships
  • Familiarity with kinetic and potential energy concepts
  • Knowledge of wave properties and energy calculations
NEXT STEPS
  • Explore the relationship between amplitude and energy in mechanical waves
  • Study the mathematical derivation of power in AC circuits
  • Investigate the principles of harmonic motion in vibrating systems
  • Learn about the implications of wave interference and energy cancellation
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Students of physics, educators teaching wave properties, and anyone interested in the mathematical foundations of energy in physical systems.

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If you have a sinusoid as voltage and R, so the phase between Voltage and current is zero.
Then also I is sinusoidal.
The power P = V x I = V sin t x I sin t = VI sin^2 t.
 
The energy of a physical system always accounts for the total energy, that is the sum of (total) kinetic energy and (total) potential energy. Kinetic energy is proportional to square of velocity. For a system that can be modeled as a vibrating spring (which is perhaps true for all sinusoidal dynamic system), the potential energy is proportional to square of displacement. That's the total energy must be proportional to square of its amplitude.
 
I guess you are the type of "yellow card" collector Adam. I'm not sure if there is a maximum limit of the number collected.
 

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