Hearing Range Test and Hearing Loss Simulator

What is the normal human audible hearing frequency range?

The normal young human ear hears sound frequencies from about 20 Hz to 20,000 Hz (20 kHz). It is most sensitive near 3.3 kHz, and tones near either end of that range must be far more intense to be heard at all. Age-related hearing loss (presbycusis) lowers the upper limit first, and the top end starts to fall in early adulthood.

A pitch is a place

Inside the cochlea, the spiral of the inner ear, runs the basilar membrane, about 35 mm long when it is unrolled. It is narrow and stiff at its base, by the middle ear, and wide and floppy at its far end, the apex. A sound sets off a wave that travels along it from the base and peaks at the one place whose stiffness matches the sound’s frequency, and the hair cells there are the ones that respond. High pitches peak near the base and low pitches near the apex, so the membrane sorts a sound into its frequencies the way a prism sorts light into colours.

Greenwood’s formula gives the place for every pitch: f = A(10^(ax) − k), with A = 165.4 Hz, a = 2.1 and k = 0.88 for the human ear, where x is how far along the membrane the place is, as a fraction of its length measured from the apex. At the apex it gives 19.85 Hz and at the base 20,677 Hz, close to the 20 Hz to 20 kHz usually quoted for young ears. That is the map this simulator draws: the ribbon at the top is the membrane unrolled, with the apex on the left so that pitch rises from left to right on the ribbon and on the chart below it alike.

Worked example: 1 kHz and 16 kHz on the ribbon

1. 1 kHz. Inverting the formula, x = log₁₀(f/A + k) / a. For 1,000 Hz, f/A + k = 6.9259, whose logarithm is 0.8405, and 0.8405 / 2.1 = 0.4002: the place is 40.0 percent of the way from the apex. On a 35 mm membrane that is (1 − 0.4002) × 35 = 21.0 mm from the base, the figure the readout and the pointer above the wave show.
2. 16 kHz. f/A + k = 97.615, whose logarithm is 1.9895, so x = 0.9474, and the place is (1 − 0.9474) × 35 = 1.8 mm from the base. Four octaves up from 1 kHz the wave has moved 19.2 mm.
3. The top octave. 10 kHz peaks 5.2 mm from the base and 20 kHz 0.24 mm from it, so the whole octave from 10 to 20 kHz occupies just 5.0 mm, the stretch nearest the middle ear.

Above about 1 kHz every octave takes nearly the same length, 4.4 mm at 1 kHz rising to 5.0 mm at 16 kHz, which is why the cochlea is often called a logarithmic frequency analyser: it breaks a sound into its frequencies, the job the Fourier series visualiser does with sines. At 100 Hz an octave gets only 2.0 mm, and everything from 20 to 100 Hz is crowded into the last 2.9 mm at the apex. The lines joining the ribbon to the chart show it: they run nearly straight down at the high end and fan out at the low end, where the chart’s even decades take far more room than the membrane gives them.

The wavelengths run from 17.15 m at 20 Hz to 1.7 cm at 20 kHz, the speed of sound divided by the frequency, as the wavelength and frequency calculator works it out. The cochlea does not hear wavelengths, though: the membrane responds to how fast the pressure changes, not to how far apart its peaks are in the air.

The threshold curves up at both ends

The shaded floor of the chart is the quietest tone a young adult can hear at each frequency in a quiet room, by Terhardt’s formula of 1979. It is lowest, −5.0 dB SPL, near 3.3 kHz, where the ear canal’s resonance helps, and 3.4 dB SPL at 1 kHz. It climbs to 83.2 dB SPL at 20 Hz, so a very low tone must be about 80 dB more intense than a 1 kHz tone to be heard at all, and to 65.9 dB SPL at 16 kHz. Above 16 kHz the formula is not used: its last term gives 105 dB at 18 kHz and 160 dB at 20 kHz, which no measurement supports. The chart dots its last stretch from 12.5 kHz, because there it already climbs faster than measured thresholds do: 41 dB from 12.5 to 16 kHz, where the 10 to 21 year olds Lee and colleagues tested in 2012 rose 21 dB.

Decibels here are dB SPL, sound pressure level against 20 micropascals. An audiogram uses dB HL instead, hearing level, which counts from the average young ear’s threshold at each frequency, so 0 dB HL is normal hearing everywhere. The decibel calculator does the arithmetic of both.

Typical upper limit by age, as a band

Age lifts the threshold at the top first. The bands at the top right of the chart come from one study: Lee and colleagues measured 352 listeners aged 10 to 65, all with normal audiograms up to 4 kHz, at 21 frequencies from 125 Hz to 20 kHz, and published the mean threshold of each age group (Ear and Hearing, 2012, Table 1). For each group the band runs from the frequency at which its mean threshold has risen 40 dB above its own threshold at 1 kHz to the one at which it has risen 60 dB: roughly where a tone that is clearly audible at 1 kHz, and played at the same level at every pitch, fades out.

It is a band, and never a single “hearing age”, for three reasons. The level at your ear is unknown, so the band spans 20 dB of it. People of the same age differ by far more than the band is wide. And an average of a group cannot say where in the group one person sits. The study’s volunteers all had normal audiograms up to 4 kHz, so these are better ears than the average for each age, and its equipment could play no more than 105 dB SPL: listeners who did not respond were recorded at that limit, which was 25 percent of them at 12.5 kHz and 84 percent at 20 kHz, so the averages near the top are floors and the true bands may sit a little lower.

How to run it well

• Wired headphones in a quiet room. Laptop and phone speakers produce little below about 100 Hz and roll off at the top, and some Bluetooth headphones compress sound in ways that cut the highest frequencies before they reach you.
• Set the level once. Play the 1 kHz reference and set your device’s volume so it is quiet but clear, then leave the volume alone. Nothing here plays more than 10 dB above the reference, and every tone fades in and out over 30 ms, because an abrupt start is a click that anyone can hear, which would fake a result at 19 kHz.
• Never chase a tone. Do not turn the volume up to find a tone you cannot hear. You may not hear it, but it can still be loud enough to harm your ears or a small speaker. This matters most for children, who hear the highest tones best.
• Know your device’s ceiling. A browser plays nothing above half its sample rate, and this page stops at 0.45 of it, where audio converters start to cut: 19,845 Hz at 44.1 kHz. The sampling and aliasing visualiser shows why. A small speaker pushed hard, or a device’s own sound processing, can also add faint sounds at lower pitches, which the ear hears far more easily: if a very high tone sounds like a lower one, or like a buzz, that is your equipment, not your hearing.

Finding your limit: the method of limits

Find my limit sweeps at the same pace as the main sweep, 20 Hz to 20 kHz in 30 s, which is 3.01 s for every one of its 9.97 octaves. Three runs start high and fall until you hear the tone; three start lower and rise until it has gone. They alternate because reaction time pulls each kind the opposite way: at a typical 0.35 s, a falling run has moved 0.12 octave past your limit before you press, and a rising run 0.12 octave beyond it, so for a true limit of 15 kHz the falling runs read 13.8 kHz and the rising ones 16.3 kHz. The estimate is the geometric mean of all six, which cancels that bias, with their spread in octaves. Two silent catch trials are mixed in at random, and a press during one is counted as a false alarm. While a run is going the pitch is hidden from the chart, so only your ears decide. The runs play 10 dB above the reference you set, the loudest this page goes, so the tone is clearly audible wherever your hearing is good, which is what the age bands assume: at a quieter level the same ears give a lower limit.

Why high pitches go first

Every sound passes the base of the cochlea on its way to its own place, and the hair cells there, which answer the highest pitches, are the first to be lost with age and with some drugs. Years of loud noise usually strike a little further in, near 4 kHz, still in the cochlea’s first turn, which is the dip the noise preset shows. Hair cells do not grow back. So the top octave, the basal 5 mm, is where hearing usually starts to fade with age, and the shrinking bands in the chart show it: the 56 to 65 year olds’ band sits more than 5 kHz below the 10 to 21 year olds’. Equipment can do the same thing without any help from the ear, which is why a missing top end on laptop speakers says nothing about your hearing.

What the hearing loss simulator does and does not do

An audiogram becomes a filter that turns each frequency down by the hearing level there: a linear-phase filter of 2,047 taps at 44.1 or 48 kHz, so every frequency is delayed by the same 23.2 ms or 21.3 ms, and the plain sound is delayed to match, so switching between with and without the loss lands on the same moment of the music. It never amplifies, and it lands within 1 dB of every point of every preset. A filter of that length cannot turn sharply at the low end, though, where the points are only a few hundred hertz apart: a step dragged by hand of more than about 30 dB between 250 and 500 Hz, or 70 dB between 500 Hz and 1 kHz, comes out smoothed, so 0 dB at 250 Hz beside 80 dB at 500 Hz gives about 69 dB at 500 Hz. Turning frequencies down can still raise a sound’s peaks, because what is left adds up differently, so the result passes a hard ceiling that holds its peaks to the level you set. The WHO grade on the audiogram is read from the average of 500, 1000, 2000 and 4000 Hz, as the World Report on Hearing (2021) grades the better ear: under 20 dB HL is normal, then mild, moderate, moderately severe, severe, profound, and complete from 95 dB HL.

The age presets are each group’s mean threshold less that of the 10 to 21 year olds, from the same study. The one for 56 to 65 year olds is only 5.9 dB HL on the four-frequency average, normal by the WHO grade, yet 26.4 dB down at 8 kHz and 58.2 dB at 12.5 kHz: listen to the hi-hats lose their shine while speech frequencies barely change.

What a filter cannot do is the rest of hearing loss. A damaged cochlea also makes loud sounds grow too fast, called loudness recruitment, and blurs nearby pitches together, because its frequency analysis loses its sharpness, as Moore sets out in Cochlear Hearing Loss (second edition, 2007). Turning sounds down copies neither, so real hearing loss is harder to listen through than this, especially speech in noise, and turning sounds up alone cannot undo it.

Why this is not a hearing test

A hearing test measures each ear separately in dB HL with an audiometer whose earphones are calibrated to known levels, in a quiet booth. This page plays sound at a level it cannot know through equipment it cannot see, so its numbers belong to your setup as much as to your ears, and it gives no pass or fail. Even a real audiogram is not the whole story: the WHO notes that the ability to detect pure tones in a quiet room is not, in itself, a reliable indicator of hearing disability. If you notice a change in your hearing, see an audiologist or a doctor, and if it came on suddenly, in one ear or both, get medical help straight away, because sudden hearing loss can need treating quickly.

The travelling wave on the ribbon

The wave is drawn, not solved. Its shape follows the sketches von Békésy made from his measurements in Experiments in Hearing (1960): an envelope that peaks at Greenwood’s place, rising gently over about 7 mm on the side towards the base and dying within about 1.5 mm beyond its peak, with the crests crowding together as the wave slows. The real wave runs at the tone’s own frequency, far too fast to see, so the drawing runs at one cycle a second. For waves on a string, where the speed is the same everywhere, the standing wave simulator is the place to look.