The relationship between amplitude and sound waves is direct. The amplitude of a sound wave refers to the maximum displacement of air particles caused by the wave's pressure variations. It is a measure of the wave's intensity or loudness.
When the amplitude of a sound wave increases, the displacement of air particles becomes greater, resulting in a more intense variation in air pressure. This increase in pressure variation leads to a higher sound intensity or louder sound.
In mathematical terms, the relationship between amplitude and the perceived loudness of a sound wave is not linear but follows a logarithmic scale. This is because human perception of loudness is not directly proportional to the physical amplitude of the sound wave. The perceived loudness increases logarithmically as the physical sound wave amplitude increases.
So, to summarize, increasing the amplitude of a sound wave leads to a higher sound intensity or louder sound.