Quarter Wave Length Resonator

The outer ear canal (external auditory meatus) is like a tube closed at one end. The length of the ear canal is roughly 2.3 cm. The fundamental resonant frequency is the lowest frequency possible with this configuration, i.e., only a quarter of the wave length can occur in that length of tube.

In order to calculate the hypothetical  resonance frequency (a.k.a. first natural mode) of a hard-walled tube closed at one end we must take the velocity divided by four times the length of the tube (in centimeters or inches). We have to do this to figure out the wavelength of one full cycle.

Therefore: the wavelength of an unknown frequency is 4 x 2.3 cm  = 9.2 cm

Velocity of sound = 34400 cm/sec

Resonant frequency = 34400 ⁄  9.2     = 3,739 Hz

The above is an idealized situation. One must remember that the walls of the external auditory meatus are not solid, and the meatus is not straight. The tympanic membrane is concave. All of these factors play a role in the resonance.

The actual resonant frequency of an average adult EAM is roughly 2700 Hz. Male resonant frequencies are usually lower that female resonances. Children resonant frequencies are higher still because of the shorter length of their EAM.

There is an advantage (boost) 12-17 dB in the amplitude of a signal at the resonant frequency. So if I were to put a small microphone in the ear canal connected to a sound level meter or other measuring device and then presented through an earphone a 70 dB level pure tone sweep through frequencies ranging from 125 Hz to 8,000 Hz, I would see an increase in the amplitude of the sound pressure level in the EAM the closer I got to 2700 where the response would peak. So the resonant frequency of the EAM is the result of a band pass filter centered at 2700 Hz. In other words, the physical characteristics of the tube closed at one end with a length of 2.3 cm allow frequencies closest to 2700 Hz to pass through while attenuating frequencies outside the band pass filter (above and below 2700 Hz).

So what?  What’s the take home message? Who really cares? Well, audiologists do because we need to take into account the acoustics of the ear canal when fitting individuals with amplification. The more we fill the EAM with an ear mold or custom hearing aid the more we alter the natural resonance of the canal. That in turn affects what gets through to the tympanic membrane and up the afferent auditory pathway.

5 comments on “Quarter Wave Length Resonator

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  2. Sop says:

    Hi, If I’m correct then adult female resonance should be greater than 2700 Hz?

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