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If the amplitude of a wave is doubled, how does this affect the energy carried b

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Question: If the amplitude of a wave is doubled, how does this affect the energy carried by the wave? (2021)

Options:

  1. Energy is halved
  2. Energy remains the same
  3. Energy is doubled
  4. Energy is quadrupled

Correct Answer: Energy is quadrupled

Exam Year: 2021

Solution: 

The energy carried by a wave is proportional to the square of the amplitude. Therefore, if the amplitude is doubled, the energy increases by a factor of four.

If the amplitude of a wave is doubled, how does this affect the energy carried b

Practice Questions

Q1
If the amplitude of a wave is doubled, how does this affect the energy carried by the wave? (2021)
  1. Energy is halved
  2. Energy remains the same
  3. Energy is doubled
  4. Energy is quadrupled

Questions & Step-by-Step Solutions

If the amplitude of a wave is doubled, how does this affect the energy carried by the wave? (2021)
  • Step 1: Understand what amplitude means. Amplitude is the height of the wave from its rest position.
  • Step 2: Know that energy in a wave is related to its amplitude. Specifically, energy is proportional to the square of the amplitude.
  • Step 3: If the amplitude is doubled, we can represent this mathematically. If the original amplitude is A, the new amplitude is 2A.
  • Step 4: Calculate the energy with the original amplitude. If the energy is E when the amplitude is A, then E is proportional to A^2.
  • Step 5: Calculate the energy with the new amplitude. The new energy with amplitude 2A is proportional to (2A)^2.
  • Step 6: Simplify (2A)^2. This equals 4A^2.
  • Step 7: Compare the new energy to the original energy. The new energy (4A^2) is four times the original energy (A^2).
  • Step 8: Conclude that if the amplitude is doubled, the energy carried by the wave increases by a factor of four.
  • Wave Energy and Amplitude – The relationship between the amplitude of a wave and the energy it carries, specifically that energy is proportional to the square of the amplitude.
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