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Question
Why energy is directly proportional to (amplitude)2 . explain it
Why energy is directly proportional to (amplitude)2 . explain it
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Solution
Dear student
A wave is a collection of simple harmonic oscillators.
The energy of a SHO equals the potential energy at maximum displacement.
The PE at maximum displacement is the work done by an external force in pushing the oscillator out from the equilibrium position to maximum displacement.
The external force acts against the oscillator's internal force which obeys Hooke's Law
F = -kx
∫ F ( x ) d x = ∫ k x d x = 1 /2 k A ^2
Energy proportional to (amplitude) 2
A wave is a collection of simple harmonic oscillators.
The energy of a SHO equals the potential energy at maximum displacement.
The PE at maximum displacement is the work done by an external force in pushing the oscillator out from the equilibrium position to maximum displacement.
The external force acts against the oscillator's internal force which obeys Hooke's Law
F = -kx
∫ F ( x ) d x = ∫ k x d x = 1 /2 k A ^2
Energy proportional to (amplitude) 2
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