May 2024 Newsletter: Bottle Top Blues

Have you ever blown across the top of a bottle to make it whistle? Did you notice how the pitch of the whistle is higher when there’s more liquid in the bottle and gets lower when there’s less liquid? That’s because the bottle is a Helmholtz resonator. Read on to learn more about the magic of this peculiar class of objects.

Resonance is a phenomenon that is characterized by vibration at a particular frequency. Every object has a resonant frequency dependent on its material, geometry, and structure. Think of a tuning fork when tapped on a surface – it makes a tone at its resonant frequency. Conversely, if you hum at that same frequency, the tuning fork will respond sympathetically. In addition to tuning forks, other objects that are intended to resonate at a particular frequency are Helmholtz resonators.

Any enclosed volume with a sufficiently small opening can be considered a Helmholtz resonator, which are named after Hermann von Helmholtz who first calculated the resonant frequency of a container in the 19th century. The resonant frequency is determined by the open volume of the container, the area of the opening, and the neck length of the opening. When air enters the container, it acts like an air-mass spring oscillator bouncing in and out of the container. The frequency at which this occurs is the resonant frequency of the open volume of the container.

Helmholtz resonators can be found everywhere. Many musical instruments are constructed with a resonant frequency in mind. With sufficient energy forcing the air to oscillate in and out of the volume of an instrument, we hear a tone. This tone can be tuned to provide an additional boost in sound at a beneficial frequency for that instrument. An example is a violin whose openings and inner volume are tuned to have a resonant frequency that boosts the sound of the lower strings. Helmholtz resonators can also be found in loudspeakers, particularly subwoofers. Many subwoofers have a small opening exposing the enclosed volume of a speaker cabinet. The volume of the speaker cabinet, the size of the opening, and the length of the opening neck can be adjusted to provide an additional boost in sound at lower frequencies and add punch to the bass.

A resonator can also be used to absorb sound. When an incident sound wave hits the opening of a resonator, energy is absorbed at the resonant frequency as the sound wave tries to oscillate the air-mass spring of the enclosed volume. If we were to place many containers with the same resonant frequency next to each other, more energy of that incident sound wave will be absorbed. A common example of this is slotted concrete masonry units present in many gymnasiums.

As acousticians, we work to understand how these resonant frequencies can be beneficial or detrimental to room acoustics. So next time you are drinking a beer with your friends, blow across the bottle tops and come up with your own tune.

Villanova University CEER Expansion Project