Doubling the amplitude of a sound wave has a significant effect on its perceived loudness. Amplitude is directly related to the intensity or energy carried by the sound wave. When the amplitude of a sound wave is doubled, the energy carried by the wave is quadrupled because the relationship between amplitude and energy is nonlinear.
Increasing the amplitude of a sound wave increases the displacement of air particles as the wave passes through the medium. This increased displacement leads to higher pressure variations, resulting in a louder sound. Therefore, doubling the amplitude of a sound wave would generally be perceived as a substantial increase in volume.
It's important to note that human perception of loudness is logarithmic rather than linear. This means that a doubling of amplitude does not necessarily result in a perceived doubling of loudness. Instead, it may be perceived as a significant increase, but not as loud as doubling the volume again. The relationship between amplitude and perceived loudness follows a psychophysical phenomenon known as the Weber-Fechner law.
In summary, doubling the amplitude of a sound wave increases its energy and can be perceived as a significant increase in loudness, although the relationship between amplitude and perceived loudness is nonlinear.