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

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

Options:

Correct Answer: Increases by a factor of 9

Solution:

Energy is proportional to the square of the amplitude, so if amplitude is tripled, energy increases by a factor of 3^2 = 9.

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

If the amplitude of a wave is tripled, 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 tripled, we can express this mathematically as 3 times the original amplitude.
Step 4: To find the new energy, we need to square the new amplitude. So, we calculate (3 * original amplitude)^2.
Step 5: This simplifies to 3^2 * (original amplitude)^2, which equals 9 times the original energy.
Step 6: Therefore, if the amplitude is tripled, the energy increases by a factor of 9.

Wave Energy and Amplitude Relationship – The energy of a wave is proportional to the square of its amplitude, meaning that changes in amplitude will affect energy in a quadratic manner.