How are amplitude and loudness related in sound waves?

Amplitude and loudness in sound waves are directly related; higher amplitude results in louder sounds.

In more detail, sound waves are longitudinal waves that travel through a medium, such as air or water. These waves are characterised by areas of compression and rarefaction, which correspond to the peaks and troughs of a wave. The amplitude of a sound wave is the maximum displacement of the particles in the medium from their equilibrium position. In simpler terms, it's the 'height' of the wave.

Loudness, on the other hand, is a subjective perception of the intensity of a sound by the human ear. It's how 'loud' or 'quiet' we perceive a sound to be. This perception is influenced by the amplitude of the sound wave. When the amplitude of a sound wave increases, the wave carries more energy. This increased energy causes the particles in the medium to vibrate more vigorously, which our ears interpret as a louder sound.

However, it's important to note that while amplitude and loudness are directly related, they are not the same thing. Amplitude is a physical, measurable quantity, while loudness is a subjective perception that can vary from person to person. Furthermore, the relationship between amplitude and loudness is not linear. Doubling the amplitude of a sound wave does not necessarily mean that the sound will be perceived as twice as loud. This is due to the logarithmic nature of our ears' sensitivity to sound, which is why sound intensity is often measured in decibels, a logarithmic scale.

In addition, other factors can also influence our perception of loudness, such as the frequency of the sound wave, the duration of the sound, and the listener's distance from the source of the sound. For instance, even if two sound waves have the same amplitude, we may perceive the one with a higher frequency as being louder. Similarly, a sound may seem quieter if we are further away from the source, even if its amplitude has not changed.