Helmholtz Resonator Calculator

Take a box, poke a hole in it: that's how you can build a rudimental resonating chamber, then use our Helmholtz resonator calculator to find the frequency it operates!

Since antiquity, humanity has built tools that help amplify or absorb sounds: the Helmholtz resonator is one of these devices. If you want to discover more about them, keep reading! You will learn:

• What a Helmholtz resonator is;
• How a Helmholtz resonator works;
• How to calculate the frequency of a Helmholtz resonator;
• The applications of Helmholtz resonance: from exhausts to musical instruments; and
• A neat experiment you can try at home.

Tune in to our Helmholtz frequency calculator!

Resonators are devices that use resonance, the property of objects to prefer a specific frequency of oscillations at which the energy transfer is particularly effective to enhance or dampen a wave.

A Helmholtz resonator is a closed (or partially closed) cavity where air oscillates at a particular standing frequency controlled by a few parameters. The result is a resonance effect widely used in acoustics: from sound absorbers to musical instruments. Let's take a look at the design of a Helmholtz resonator!

The shape of the resonator itself doesn't really matter; theoretically, any shape of the cavity works. Helmholtz (a German physicist) invented the original resonator, which used an almost spherical cavity to pick up a specific frequency from a complex sound, isolating it from the rest. A small opening in the cavity allowed the experimenter to listen to that specific frequency.

When the Helmholtz resonator is used to pick up a sound, the cavity should have a larger opening from which the sound "enters". Inside the cavity, the pressure increases because of the soundwave entering it, and decreases thanks to the inertia of air when it bounces in the cavity, doing so at a specific frequency. The user can use a smaller opening to listen to the sound inside the cavity.

Helmholtz resonators can also work as sound absorbers: in this case, there is no "listening" opening. The resonator design makes it "focus" at a specific frequency, trapping it in the chamber where it eventually gets dissipated after multiple reflections inside the resonator.

If appropriately designed, a Helmholtz resonator can almost entirely erase a frequency from a room where a complex sound is reproduced.

To calculate the Helmholtz resonator frequency, you need to know a few parameters of the resonator's design. Let's take at the formula first:

where:

• $c$ – Speed of the sound in the medium (i.e., air). Its value is taken as $344\ \text{m}\!\cdot\!\text{s}^{-1}$;
• $A_0$ – Cross-section of the opening that picks the sound;
• $V$ – Volume of the resonator; and
• $L_0$ – Depth of the opening.

The depth of the opening may take into account the end correction of a hole in acoustics: that's a factor added to the length to justify the different starting point of the soundwave in the opening itself. The following formula gives the end correction:

where $L$ is the true length of the opening and $ΔL$ is the end correction.

The name Helmholtz resonator may sound highly technical, but we are almost sure you met them already without knowing it!

The first example of a Helmholtz resonator is... a bottle! When you take a bottle, and blow over the open neck, you hear a sound, a single note, usually pretty low: that's the resonating frequency of the bottle. Blowing right above the neck creates the difference in pressure necessary to make the air inside the bottle vibrate: that's an interesting variation on the functioning of a Helmholtz resonator.

Fill the bottle (or empty it) with a liquid, and you will hear the frequency shift: the emptier the bottle, the lower the frequency. Check the formula for the resonating frequency: the volume of the resonator is at the denominator of the fraction!

Many musical instruments make use of Helmholtz resonators. The examples range from acoustic guitars, where the wooden body helps amplify the sounds, to ocarinas, which are almost ideal Helmholtz resonators.

In ocarinas, the different notes are obtained by closing or opening holes with the fingers, thus changing the value of $A_0$.

Helmholtz resonators excel in muffling sounds when designing concert rooms or studios. In those cases, once sound engineers identify a problematic frequency, they design the proper resonator that absorbs that particular tone. Another application of Helmholtz resonance is in the exhausts of vehicles: creating a suitably sized exhaust allows to filter the unwanted noises from the engine. Or to amplify them, even if no one likes that.

One last example! Have you ever tried listening to a seashell? The sound you hear, commonly called the "sound of the sea", is the effect of Helmholtz's resonance: the internal structure of the shell makes it an astonishingly good resonator, and you can hear only some specific frequencies. 🐚

Our Helmholtz resonator calculator allows you to calculate the value of the Helmholtz resonance frequency for various combinations of shapes and openings. Let's take a look at it.

1. Choose the type of chamber you are considering. We offer you four different possibilities:

   • Arbitrary shape;

   • Parallelepipedal shape;

   • Spherical shape; and

   • Cylindrical shape.

   In the first one, you have to manually insert the volume (you can calculate it for many shapes with our volume calculator, while for the others, we are the ones doing the math — you only have to insert the measurement of the chamber.

2. Then, you have to choose the type of opening you are considering. Here you have three choices:

   • Arbitrarily shaped opening;

   • Circular opening; and

   • Rectangular opening.

   Choose the one that fits your problem better and insert the measurements if necessary.

3. Finally, insert the value of the length of the opening. It is crucial for a satisfying outcome of the calculations.

We got really excited to see that there is an exceptionally simple experiment you can make at home to test our Helmholtz resonator calculator. You will only need an empty bottle and a tape meter.

The bottle should have a shape made of a composition of elementary shapes, like sphere and cylinder. Take the measurements you will need:

• Circumference of the bottle;
• Height of the cylindrical part;
• Diameter of the opening (where the cork sits, to be clear);
• Length of the neck.

Now calculate the volume of the bottle. You can use our calculators to do it faster: go to our sphere volume calculator and cylinder volume calculator!

We found that our bottle, with a circumference of $23.5\ \text{cm}$, and a height of the cylindrical section equal to $16.5\ \text{cm}$ has a volume of:

The neck has the radius of $0.95\ \text{cm}$ and the length of $7.5\ \text{cm}$.

Insert these measurements in our calculator after selecting arbitrary shape in the resonator shape section, and circular opening in the opening section. The result you will find is:

Install an application that allows you to detect the frequency of a sound. We used this application for Android, but you can easily use an online tool like this pitch detector.

Blow on the bottle and read the measurement: we got $117\ \text{Hz}$! Science works!

The Helmholtz resonator frequency equation is fᵣₑ= c/2π × √(A₀/(V × L₀)), where c is the speed of sound in air (344 m/s), and A₀, L₀, V are the geometrical parameters of the resonator: the area and length of the opening, and the volume of the chamber.

A Helmholtz resonator is a device able to pick up a single frequency (the Helmholtz resonance frequency), and amplify or suppress it, depending on the configuration of the resonance chamber.

The chamber's volume and one or more openings determine the frequency at which the air inside the resonator vibrates according to the standing waves contained there.

Find out more at omnicalculator.com!

The noise of an engine can be reduced noticeably using a carefully designed Helmholtz resonator exhaust able to absorb and dissipate the problematic frequencies. Helmholtz resonators in exhausts are also used to enhance a particular note from the engine: this is a common modification in car tuning.

Helmholtz resonance is a widespread acoustic phenomenon. You can experience it in many situations: from blowing on a bottle to keeping your car window open while driving, the appearance of a fixed frequency sound is associated with the existence of a resonance frequency for every cavity, which can produce a sound in the right conditions.