If the amplitude of a wave is doubled, how does the energy of the wave change?

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Question: If the amplitude of a wave is doubled, how does the energy of the wave change?

Options:

Correct Answer: Increases by a factor of four

Solution:

The energy of a wave is proportional to the square of the amplitude. If the amplitude is doubled, the energy increases by a factor of 2^2 = 4.

If the amplitude of a wave is doubled, how does the energy of the wave change?

If the amplitude of a wave is doubled, how does the energy of the wave change?

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 (4A^2) to the original energy (A^2). The new energy is 4 times the original energy.
Step 8: Conclude that if the amplitude is doubled, the energy increases by a factor of 4.

Wave Energy and Amplitude Relationship – The energy of a wave is proportional to the square of its amplitude, meaning if the amplitude increases, the energy increases by the square of that increase.