From an energy standpoint

Sound, when emitted from an instrument, travels as a longitudinal wave, but can nonetheless be modeled as a transverse wave. Therefore, all mentions of waves on this page are assumed to be transverse. Because sound can be considered transverse waves, the vibration of sound waves can be modeled and observed as the oscillation of a mass on a spring is observed.

Rigidity

For an object to oscillate, it must have a rigid and stiff structure so as to provide a restoring force to maintain vibration.

Springlike behavior

A system composed of a spring and a mass exist at rest in a natural state of undisturbed equilibrium. When the mass is acted on (by inertia) and drawn from this position, it accrues and amount of potential energy, which is directly related to the distance to which the mass is stretched. When the mass is released, the potential energy is transformed into kinetic energy as the restoring force of the spring draws the mass towards the equilibrium point. Due to inertia, however, the present kinetic energy causes the mass to overshoot the equilibrium position and displace itself to a distance where the restoring force is equal to the kinetic energy. At this point and instant, all the kinetic energy is transformed into potential energy, thus causing the motion to halt. Immediately following, however, the potential energy changes again into kinetic energy and is pulled, by the restoring force, back to toward the equilibrium position (which it overshoots again and repeat this cycle).

In a frictionless world, this cycle would repeat endlessly, and thus, the coinciding sound would ring on indefinitely.

Due to dampening properties, however, energy in the system is gradually lost and the mass will eventually settle back on its equilibrium position. Effectually, this loss of energy results in a decrease in amplitude over time, and is observed in the loss of volume of a tone that would follow coincidentally.

Vibrations can be dampened by friction, surroundings, or internally (vibrations transformed into heat).

Practical scenario(s)

A sound wave loses energy as it propagates further and further away from its source. While the emitted tone loses its intensity/volume, it does not lose its pitch/frequency.

While lost intensity doesn’t affect the pitch of a tone, it does affect the quality of the tone. This is why the cut off (the sudden end or stoppage of a note) can be almost more difficult than sustaining the note. If the intensity is not maintained and released with an upward projection, to raise the energy behind the note, then the note is dampened to quickly and dies. The diminishing resonance of the note goes flat and ruins the sound.