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If the amplitude of a wave is doubled, what happens to its energy?

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Question: If the amplitude of a wave is doubled, what happens to its energy?

Options:

  1. Remains the same
  2. Doubles
  3. Increases by a factor of four
  4. Increases by a factor of eight

Correct Answer: Increases by a factor of four

Solution: 

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

If the amplitude of a wave is doubled, what happens to its energy?

Practice Questions

Q1
If the amplitude of a wave is doubled, what happens to its energy?
  1. Remains the same
  2. Doubles
  3. Increases by a factor of four
  4. Increases by a factor of eight

Questions & Step-by-Step Solutions

If the amplitude of a wave is doubled, what happens to its energy?
  • 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 when the amplitude is 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 increases by a factor of four.
  • Wave Energy and Amplitude Relationship – The energy of a wave is proportional to the square of its amplitude, meaning that changes in amplitude significantly affect energy.
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