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Omnikalc

Ear canal resonance calculator (quarter-wave tube)

Enter the length and radius of the ear canal, the temperature and the residual canal length left by an earmold to get the speed of sound, the first resonance, the third resonance and the shifted resonance of the occluded ear.

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°C

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Results

First resonance of the open canal

2,923 Hz

Within the usual adult range of 2.5 to 3.2 kHz
Speed of sound
351.9 m/s
Third resonance of the open canal
8,768 Hz
Wavelength at the first resonance
120 mm
Resonance with an earmold in place
6,239 Hz

The ear canal resonance calculator gives the speed of sound, the first and third resonance of the open ear canal and the resonance with an earmold from the length and radius of the canal and the temperature.

How the calculation works

  • Enter the length and the radius of the canal.
  • Enter the temperature and the residual length with an earmold.
  • Read the resonances.

Example

At 35 °C the speed of sound is 331.3 × √(1 + 35 / 273.15) = 351.9 m/s. A canal of 28 mm with a radius of 3.5 mm has an effective length of 28 + 0.6 × 3.5 = 30.1 mm, so the first resonance is 351.9 / (4 × 0.0301) = 2,923 Hz, and the third is 8,768 Hz. With an earmold that leaves 12 mm, the resonance moves to 6,239 Hz.

Why it matters

The calculator helps audiology students, hearing aid fitters, acoustics students and curious people who want to understand why the ear is most sensitive near 3 kHz and why a blocked ear sounds different.

Good to know

The model is a uniform tube and a real canal is curved, has a changing section and ends at an eardrum that is not a rigid wall, so the real response is broader and a little lower than the computed value. The concha and the outer ear add their own resonance near 5 kHz, and the sum of the effects is the response of the open ear, which peaks near 2.7 kHz with a gain of 15 to 20 dB. The canal of a newborn is only about 15 millimeters long, so its resonance is near 5 to 6 kHz and moves down as the child grows, which is one reason why hearing aid settings for children are adjusted often. The speed of sound grows with the temperature, and the air in the canal is nearer to the body temperature than the room. The model also explains the occlusion effect, where a blocked canal changes the own voice and the resonances. Real ear measurements with a probe microphone are used to check the actual response of a hearing aid in the ear of the user.

The NAL-R calculator gives hearing aid gain, the tympanometry calculator treats the middle ear, the critical band calculator treats the frequency analysis of the ear and the Helmholtz resonator calculator treats another acoustic resonance.

Frequently asked questions

Why is the ear canal a resonator?

The canal is a tube closed at one end by the eardrum and open at the other, like a quarter-wave resonator. It resonates when its length is a quarter of the wavelength, which gives f = c / 4L. This boosts the sound by 10 to 20 dB around 3 kHz.

What is the end correction?

The air just outside the open end moves with the air in the tube, so the effective length is a little longer than the real one, by about 0.6 times the radius. The correction lowers the resonance by a few percent.

What does an earmold do?

A mold or an earplug shortens the open part of the canal, so the resonance moves to much higher frequencies and the natural boost around 3 kHz is lost. This is why modern hearing aids try to restore the missing high frequencies.

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Results are estimates provided for information purposes. They do not replace professional advice.

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