The Physics

Sound

Sound is energy produced by vibrations. If an object is disturbed — say, a guitar string is plucked — it begins to vibrate. This causes surrounding air molecules to vibrate, which cause other surrounding air molecules to vibrate and so on. These periodic vibrations, characterized by sound waves, travel to our ears, which we perceive as sound. Sound is characterized by two distinct components: amplitude and frequency. The amplitude determines the loudness of the sound while the frequency determines the pitch.

Natural Frequency and Resonance

We are all aware of the infamous shattering of a wine glass with just sound (watch it here). Here, I will delve into the physics behind the phenomenon.

Any and every object, when disturbed, tends to vibrate at a natural frequency (or set of frequencies), which is the speed of vibrations. If I tap a wine glass, the glass begins to vibrate at its natural frequency, causing the surrounding air particles to vibrate at the same frequency, which then travels to my ears as sound. It is interesting to note that, despite a soft tap or a hard tap, the glass has the same natural frequency — that is, the pitch of the resulting sound remains constant. What changes is the loudness (or amplitude) of the sound. The amplitude of the vibrations depends on how hard I tap the glass. A hard tap causes the glass to vibrate at large amplitudes, generating a loud sound. A soft tap yields a quiet sound. In all cases, the frequency of the sound remains the same.

If I now introduce an external sound that is tuned to match the natural frequency of the wine glass, the wine glass will be set into vibrational motion at high amplitudes. This phenomenon is known as resonance. This is quite remarkable: I am able to vibrate the glass at large amplitudes using only sound! The louder the sound — namely, the higher the amplitude of the sound — the higher the amplitude of the vibrational motion of the glass. If this vibrational motion is strong enough, the wine glass will shatter. If the sound's frequency does not match the natural frequency of the wine glass, resonance will not be observed. The vibrational amplitudes of the glass will be small. Resonance is special because it causes vibrations with large amplitudes.

Helmholtz Resonators

A Helmholtz resonator is a container of air (or some other gas) with an opening. These resonators carry just one natural frequency. It is well known that blowing into a water/pop bottle, which is a common Helmholtz resonator, produces an audible sound. This is simply the natural frequency of the resonator. When I tap a wineglass, I cause the glass to vibrate at its natural frequency. When I blow into a bottle, I cause the air inside to vibrate at the resonator's natural frequency.

On a molecular level, the vibration of the air can be explained by its "springiness." When air is blown into the resonator, the air inside is compressed. The pressure inside then forces the air out — however, due to the momentum of the outflow, a little more air is driven out than the amount originally blown in. This, in turn, creates "suction" inside the bottle, causing air to flow back in. The process continues to repeat until equilibrium is reestablished. The movement of the air going in and out is essentially a vibration that is perceived by us as sound. The frequency of this sound depends on the shape and size of the bottle.