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A Helmholtz Resonator: attenuation vs. amplification

  1. Dec 6, 2017 #1
    Hello guys,
    I read the other threads about HR, resonances and so on, but I couldn't find a clear explanation of what the practical implications of using a HR are.

    From one side, HR is described as a "reactive element", used in several contexts to attenuate a specific noise by means of reflection (phase cancellation).
    From the other side, HR is used as a "sound amplifier", used in all sort of musical instruments to amplify their sound.

    My questions are:

    1) A HR is characterized by a very narrow-band resonance, used to address unwanted noise components. However, if that is a proper resonance, that should in theory amplify that frequency instead of dampen it!
    Can you help explaining this phenomenon?

    2) Each HR has a very narrow-band resonance, therefore it could "amplify" only a single tonal component. However, acoustic guitar/bass bodies effectively and uniformly amplify a wide range of sounds, without any notch or "blind spot" due to the HR noise-cancelling effect.
    How does this phenomenon relate to the HR theory?
  2. jcsd
  3. Dec 6, 2017 #2
    When you say 'amplify' I hope you don't mean it puts out more energy than it inputs.

    In old timey American music one instrument was the gallon whisky jug which produced a low tone when blown across the open end. That just allows a buildup of sonar energy but in a smaller wavelength band. It would not go 1 watt in and 10 watts out. It would go 1 watt of say, white noise, sound across a very wide frequency band into some fraction of that one watt given out in the tone the bottle produces. Shotgun mics use this effect by having several tubes tuned to different wavelengths of sound which reinforces the voltage given out by the mic in a prefered band, usually the 3 khz region of the human voice.
  4. Dec 6, 2017 #3


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    The HR consists of a spring, which is the air in the container, and a mass, which is the slug of air in the neck. These two have a resonant frequency like a
    mass hanging on a spring. It is very easy to move such a mass at the resonant frequency - the arrangement resembles a series resonant circuit.
    The HR can have a narrow spout at the opposite end to the neck. When the spout is placed in the ear, the HR acts as a sharp bandpass filter and can pick out sounds having the same frequency as the HR resonance. The ear spout seems to not alter the resonance very much, and presumably provides a high pressure, small displacement output suitable for the ear drum.
    If used to absorb sound, the HR aperture must look like a hole in the wall of the room at that single frequency. This is because the inertia of the air slug is tuned out by the air spring. Such a hole will have a much larger effect than just its surface area.
    The violin body seems to be an HR, and I believe it is tuned near the low frequency end of the instrument to enhance that part of the spectrum. My guess is that the HR absorbs sound via the air slug in the neck, and transforms this to high pressure on the walls of the container. As these walls are flexible to some extent, they will then flex and re-radiate that sound, utilising much more surface area than that of the original string.
    I presume that at higher frequencies, the body of a stringed instrument vibrates due to sound "conduction".
  5. Dec 6, 2017 #4


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    I think the term "amplifier" is not always appropriate for an HR. An amplifier is, in the general usage of the term, a device which takes an input signal and an external Power Source to produce an output signal that is of higher Power than the input signal.
    A simple resonator does not do this because it has no Power Source. A resonator achieves an improved Matching of the source impedance to the impedance of the propagation medium (Sound in air, Radio Waves in space or along a cable etc). An HR is basically a resonator so, for instance, when its used in a loudspeaker, it just improves matching at low frequencies of a small diameter drive unit to the air, without needing to use a massive horn. The sound is launched better into the air.
    When a Jug is used as an instrument, the mechanism is slightly different because the supplied energy is in the form of a current of air ('a DC source') and the air flow is modulated by the varying pressure at the spout (due to the sound resonating in the Jug) and the impedance of the air flow from the lips. It is an Oscillator, rather than an Amplifier or just a Filter because it involves a non-linearity. The same sort of thing happens with a reed instrument, a brass instrument or a bowed string. In each case, energy is transferred from a steady input (breath or moving bow) in pulses as the resonator interacts with a non-linear element. I think the term 'relaxation oscillator' can be applied to this sort of oscillation. It is different for a plucked or struck instrument which has all the energy injected at the start and then it oscillates freely; the matching of the sound board etc. makes it louder.
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