What is the effect on the intensity if the amplitude of a wave triples?

When considering the relationship between amplitude and intensity in wave physics, it's important to understand how intensity is mathematically related to amplitude. Intensity is proportional to the square of the amplitude. Therefore, if the amplitude of a wave triples, the new intensity can be calculated as follows:

If the original amplitude is represented as A, then when it triples, the new amplitude becomes 3A. The intensity (I) is given by the formula:

I ∝ A²

Thus, if the amplitude is tripled (to 3A), the new intensity would be:

I' ∝ (3A)² = 9A²

This demonstrates that when the amplitude triples, the intensity becomes nine times greater than the original intensity. Understanding this relationship is critical in fields such as sonography, where manipulating wave amplitudes directly impacts the intensity of the ultrasound waves being used for imaging.