Helmholtz Resonator

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Helmholtz Resonator

• Emily Strauss

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• 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.

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• 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.

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

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• 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? maintaining the motion
  of the molecule
• Specific properties of its mass (M) and
  elasticity (K) determine the vibratory frequency

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• Mass
• Weight divided by the value of acceleration due
  to gravity (constant, 9.8 meters/s2)
• M weight/go
• 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

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• 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)

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• 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

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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

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• 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

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• 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 Ma (acoustic mass)
• Lengthening of the neck (increasing l)
• 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

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• The bowl of a resonator contains a volume of air
  that behaves like a spring when a force is
  applied to it
• Acoustic Compliance (Ca) inverse of the
  stiffness properties of the volume of air
• Increase stiffness decrease compliance
• Decrease stiffness increase compliance
• Increase in Ca decreases fr
• Ca can also be changed by changing the size of
  the bowl
• Larger bowls are more compliant

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• Adding Mass (Ma)? increases the period and
  decreases the frequency
• Increasing Stiffness (decreasing Ca) ? decreases
  the period and increases the frequency
• Increasing Ca ? decreases the frequency

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• 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.

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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.