Helmholtz Resonator

Emily Strauss

• Frequency was one of the topics we discussed in class. We talked about vibratory frequency, and the relationship between period and frequency. We talked about how they have an inverse relationship, so that when you double the frequency, you halve the period. When you double the period, you halve the frequency. A Helmholtz resonator is a tool that measures acoustic frequency and resonance. This presentation will explore and explain exactly what resonance is, and how a Helmholtz resonator measures it.

• • • Helmholtz Resonators are a type of filter (or resonator) for resonance: Resonance: the phenomenon whereby an object vibrates with maximum energy at a particular frequency (natural frequency) “An object has a natural frequency” means it has a frequency that naturally produces a vibration of greatest amplitude, even while other frequencies produce vibrations of lesser amplitude.

• A simple spring-mass model can be used to explain the concept of resonance

• The relative values of mass (M) and elasticity (K) determine the frequency of vibration of the simple spring-mass model – M and K of air molecule  of the molecule maintaining the motion – Specific properties of its mass (M) and elasticity (K) determine the vibratory frequency

• • Mass – Weight divided by the value of acceleration due to gravity (constant, 9.8 meters/s 2 ) • M = weight/g o –

Proportional to Weight

– Objects with mass have the property of inertia •

Inertia: opposes acceleration and deceleration

Both recoil and inertial forces are acting at the same time during vibration – One or the other dominating, depending on the position of the vibratory object • When recoil forces overcome inertial forces: – Reverse the direction of the movement back toward the rest position – Molecule does not reach full speed immediately because the inertial forces oppose acceleration

• • In spring-mass model:

If M is the heavier one:

– Greater inertial forces (greater opposition) – Where the direction of motion is reversed, the greater time required to initiate movement – More time to complete one cycle: longer period – Lower frequency • • • Adding Mass: – Increases period – Decreases frequency Stiffness (K) – Elasticity is measured in stiffness (K) – The amount of force required to displace the object some distance K = Force/Distance (in meters)

• • • • Stiffness (K) Greater recoil force associated with greater rates of movement when the forces are permitted to produce motion Motion of the spring-mass model is faster with a stiffer spring – Less time to move back and forth Increasing stiffness = decrease period = increase in frequency • All other things being equal, an increase in stiffness will increase the resonant frequency of a vibratory object

The effects of mass and stiffness (elasticity) on a resonant system

• • Adding Mass: – Increases period – Decreases the frequency Increasing Stiffness – Decreases the period – Increases the frequency

• The neck of the Helmholtz Resonator contains a column, or plug of air, that behaves like a mass when a force is applied to it • The bowl of a resonator contains a volume of air that behaves like a spring when a force is applied to it

• The neck of the Helmholtz Resonator contains a column, or plug of air, that behaves like a mass when a force is applied to it • Two ways to increase M a (acoustic mass) 1. Lengthening of the neck (increasing l) 2. Narrowing the neck opening (decreasing a) • Narrower the neck, higher speed of the molecules • Greater acceleration and deceleration effects required  increased period • Narrowing reduces resonant frequency

• The bowl of a resonator contains a volume of air that behaves like a spring when a force is applied to it • • •

Acoustic Compliance (C

– a ): inverse of the stiffness properties of the volume of air Increase stiffness = decrease compliance – Decrease stiffness = increase compliance Increase in C a decreases f

r

C a can also be changed by changing the size of the bowl –

Larger bowls are more compliant

• • • Adding Mass (M a )  increases the period and decreases the frequency Increasing Stiffness (decreasing C a )  decreases the period and increases the frequency Increasing C a  decreases the frequency

• My major is communication sciences and disorders, which simplifies to speech pathology. My major involves a great deal of study of the function and dysfunction of the vocal folds. This requires a lot of study of frequency, vibration, forces, and acoustics. Doing this project definitely improved my understanding of the relationship between physics and acoustics, and helped me to better understanding the concept of frequency. It also definitely improved my understanding of how Helmholtz resonators function.

Bibliography

-general understanding of acoustics comes from courses in acoustics. Hixon, Thomas J., Gary Weismer, and Jeannette D. Hoit. Preclinical Speech Science: Anatomy, Physiology, Acoustics, Perception. San Diego, CA: Plural Pub., 2014. Print.