In general, the amplitude of a wave is directly related to the loudness of a sound wave. When the amplitude of a wave is doubled, the resulting sound is perceived as being louder.
Loudness is a subjective perception of sound intensity, and it is closely associated with the amplitude of the sound wave. As the amplitude of a sound wave increases, more energy is being transferred, resulting in a stronger wave and a louder sound. This is because the amplitude of a wave corresponds to the amount of displacement or compression of the air molecules, which directly affects the intensity of the sound.
It's worth noting that the relationship between amplitude and perceived loudness is not a linear one. Human perception of loudness follows a logarithmic scale, known as the decibel scale. On the decibel scale, a doubling of the amplitude corresponds roughly to a 10-decibel increase in loudness. So doubling the amplitude of a wave will result in a noticeable increase in loudness, but not necessarily a doubling of the perceived loudness.