Question

How is loudness related to the amplitude of a wave?

Answer 1

The ratio of the intensity of any given sound to the intensity at the hearing threshold is used to determine the loudness of a sound. The amplitude of a wave is the distance between its highest point (peak or crest) and its lowest point (trough) (trough).

Complete Step By Step Answer:
Sound, which is a form of energy, is produced by vibrations. The molecules in the air around an object vibrate when it vibrates. When these molecules collide with molecules nearby, they cause them to vibrate as well.
Sound waves with a lot of energy have a bigger amplitude, which increases the wave's volume. The louder the sound, the higher the amplitude of the wave, and the softer the sound, the smaller the amplitude of the wave.
When a body vibrates with a bigger amplitude, it emits more energy, which is received by the eardrum in significant amounts, making the sound appear louder.
$loudness \propto {(amplitude)^2}$
This is the relation between loudness and amplitude.
A sound wave's amplitude is proportional to pressure fluctuations. The sound is heard as louder as the amplitude grows, and as quieter as the amplitude decreases.

Note:
A sound wave's particles move back and forth rather than up and down. The pattern of a wave repeats itself. One entire repetition is defined as a cycle. A cycle's period is the amount of time it takes to complete. Frequency is known as the number of cycles per second.