If we double the amplitude of a sound wave while keeping all other factors constant, such as wavelength and speed, the intensity of the sound wave will increase by a factor of four.
The intensity of a sound wave is directly proportional to the square of its amplitude. Mathematically, the relationship between intensity (I) and amplitude (A) is given by:
I ∝ A^2
This means that if we double the amplitude (A), the intensity (I) will be four times greater. In other words, the intensity increases by a factor of four (2^2 = 4).
Doubling the amplitude of a sound wave corresponds to increasing its energy and, consequently, the power carried by the wave. This increase in power results in a higher intensity of the sound wave, which can be perceived as a louder sound.