If the amplitude of a wave is increased threefold, by what factor will the power increase?

The relationship between amplitude and power in a wave is governed by the formula for power, which is proportional to the square of the amplitude. When the amplitude of a wave is increased, the power increases according to the formula:

Power ∝ Amplitude²

Therefore, when the amplitude is increased threefold, the new amplitude becomes 3A (where A is the original amplitude). The new power can be calculated as follows:

New Power ∝ (3A)² = 9A²

This demonstrates that the power increases by a factor of 9 when the amplitude is increased threefold. Hence, the correct answer reflects this squared relationship, indicating that if the amplitude triples, the power will increase ninefold.