# Why is it so easy to create audible sound?

## Context

Why is it so easy to create audible sounds in life with basically anything?

• Putting your cup of coffee on a table comes with a sound
• Turning a page of your book comes with a sound
• Even something as soft as a towel creates sound when you move it or unfold it.
• When leaves on the ground are moved by wind, one hears the sound!
• Of course the list doesn't have an end, but you get the point.

My own guess is that: it must be related to the average density of air around us, which as it so happens, makes air compression caused by our day-to-day activities audible. The fact that our hearing frequency range extends from 20 Hz to 20,000 Hz is most probably due to evolutionary reasons, namely that those with poorer hearing range had a harder time to survive. But that's another story.

## Question

All that aside, what criteria need to be fulfilled for an acoustic sound to be audible? i.e. fit into our hearing range. I would imagine that for a complete picture of the problem, there are many factors to consider e.g. :

• Density of the object $\rho_o$ creating the sound
• Density of air $\rho_{\rm air}$, for simplicity let's assume it is constant, i.e. fixed latitude!
• Speed $v$ of the moving object
• The object's cross section $S$ (probably a very crucial factor as it goes hand in hand with the intensity of the acoustic wave I'd imagine)
• The object's surface details: rough, soft, hard, flat etc.

Any back of the envelope estimation with the minimum necessary number of factors to take into account will do fine!

• Most people can't actually hear all the way from 20Hz to 20kHz. At the bottom end, it's more a rumble than a sound. At the top, few people can hear that high, and the top frequency drops with age. – Simon B Dec 23 '14 at 15:21
• It’s probably because sound that was easy to produce became audible during evolution ;-) – mirabilos Dec 23 '14 at 17:10
• @user929304 The edit is not done for "no reason". The HTML <hr> element represents a thematic break between paragraph-level elements; it's not a line used for decoration. – Blackhole Dec 23 '14 at 17:56
• @Blackhole: Yet absolutely everything else about the edit was completely superfluous. – Lightness Races in Orbit Dec 23 '14 at 18:19
• This is not a physics question. 'Audible' is defined by the observer. The observer's instruments are determined by evolution. Hearing is more useful if it detects common signals, and would be more likely to be passed on to later generations. – Henk Langeveld Dec 23 '14 at 21:02

We can consider four aspects of your question:

1. Why do most events generate sound?
2. What sounds get propagated?
3. What does it take for sound to be detected?
4. Has evolution got anything to do with this?

1 - generating sound Most of the sounds you describe are "broad band". Remember that a delta pulse (short sharp shock) is basically "all frequencies", although in reality a pulse of finite duration will not contain the very highest frequencies. Now it turns out (see for example my earlier answer on this topic) that it takes an absolutely TINY motion (less than an atom's width) to generate an audible sound pulse - so we can safely say "every motion makes a sound; most motions make audible sound".

2 - propagation of sound Like all finite-sized sources of energy, once you are a reasonable distance (reasonable compared to the size of the object generating the sound) away, sound intensity falls off as the inverse square of the distance (barring mechanisms to contain the direction of propagation: tunnels, mountains etc). This means that sound will typically remain audible for roughly the same distance as the object making it remains visible/interesting. Certain very loud sources (e.g. crickets) are an exception to this rule - but they are deliberately trying to be heard a long way off (see point 4). Sound is also attenuated by air - according to Stokes's Law, the attenuation coefficient $\alpha \propto \omega^2$, meaning that higher frequencies are absorbed more strongly (because of viscous interactions in the air). From the Bruell & Kjaer website:

Low frequencies really only get attenuated according to the inverse square law, but higher frequencies are attenuated more strongly.

3 - detecting sound In order to detect sound, a membrane needs to be moved. This motion then has to somehow be conveyed to the nervous system, which is water-based and therefore has a very different acoustic impedance than air ($z_0 = \rho c$ - so when density increases by 1000x and speed of sound by 4x, you have a mismatch...). The mechanisms in the ear (tympanic membrane, malleus, incus, stapes, oval window, cochlea) is a beautiful piece of engineering to create something of an acoustic match, and works quite well over a range of frequencies. Unfortunately, for very low or very high frequencies, bit of that mechanism stop working so well - the finite mass (inertia) of the components makes them more reluctant to move at high frequencies. This again puts an upper limit on the frequency we can hear. However, the "amplification" that the entire organ provides is exquisite - as I computed in the answer linked above this means you can hear tiny, tiny vibrations.

4 - evolution The human body is a wonderful machine, refined by aeons of evolution - "she who hears the approaching predator lives to procreate another day". The combination of "everything disturbs the air around it" and "we are designed to detect the slightest sound" is the answer to your question.

• @Brionius - my point is that there is a place where a vibration is turned into a nerve stimulus - and at that point you are interacting with material with a very different acoustic impedance than you started with. The series of mechanical "devices" that enact this transformation is stunningly complex and beautiful. The oval window transmits the vibrations to liquid inside the semicircular canal in the cochlea, which completes the transformation to the "liquid phase". And that's where the hair cells in the organ of Corti vibrate, and stimulate the nerves (doing a Fourier Transform on the way). – Floris Dec 23 '14 at 18:36
• @Floris Well done on tackling different aspect of the question. One bit that was a bit mind-boggling to me: "it takes an absolutely TINY motion (less than an atom's width) to generate an audible sound pulse", half an Angstrom? wow, would you care to expand a bit more on this? where is it coming from? – Phonon Dec 24 '14 at 10:52
• @Phonon - thanks. See my earlier answer where I do the math to link displacement to audible sound. It is indeed mind boggling. – Floris Dec 24 '14 at 12:00
• @Floris yes most definitely, I was just stretching to the dark with this idea because it's so so fascinating :). I have to share this Feynman bit with you. – Phonon Dec 24 '14 at 12:47
• @Phonon thanks for sharing. Love the twinkle in his eyes...! – Floris Dec 24 '14 at 12:55

So, we need data of from ears. An audible sound has an minimum intensity of $I_0\approx10^{-12}W/m^2$. This shows how sensitive our ears really are. A way to see it is to use that intensity to calculate the total variation of air displacement. If you do that, we will have about $\Delta u\approx1.1\cdot 10^{−11}m$. This is $0.11$ angstroms! This is smaller than the radius of atoms!! For comparisom, the hydrogen atom in the lowest energy state has radius of $0.52$ angstroms. So, our ears are an extraordinary amazing "device" very, very, very sensitive, cabable of detecting this magnitudes of displacements of the eardrum. This relates intensity of the wave and the maximum air displacement $U$: $$I = \frac{1}{2}\rho_{air}v\omega^2 U^2$$

Where, $v$ is the speed of sound. The frequency is $f = \omega/2\pi$.

Another fact to consider, is frequency. Our ear can hear from $f_m=20Hz$ to $f_M=20kHz$. When we "putting your cup of coffee on a table", for example, we deform the table. The table will vibrate for a few seconds. This vibration will vibrate the air as well, which will travel as a wave until reach your ears. Then you hear it. Those vibrations are very small, but our ear can detect it. Those vibration frequencies almost all time at some moment are in range $f_m<f<f_M$. Then we hear it.

• Things like this force me to consider the Glory of the natural world. When we communicate with one another we blast air through space into tiny holes in the sides of our heads that measure vibrating molecules. It's almost surreal. – easymoden00b Dec 23 '14 at 16:45

The density of air is well below that of most solids, so any solid object that is vibrating will vibrate the air around it.

If you bash a solid object, it will vibrate at a frequency dependent on it's mass and elasticity (amongst other things). Many everyday objects have a resonant frequency within the range of human hearing. Even if you can't hear the resonant frequency of the object, then you may still hear harmonics, or the resonance of parts of the object.

• Well done. May I suggest adding a little info about impulse/shock waves, which don't depend so much on internal resonance as they do on air being expelled from the volume around the point of impact? – Carl Witthoft Dec 23 '14 at 15:28
• Turning around your first sentence: If the density of air is well below that of most solids (including the moving components of the ear), does this imply that vibrating air will have a hard time inducing vibration in the moving components of the ear? From my simplistic viewpoint this would appear to be an inconsistency in your answer - I'd love to see it clarified. – Digital Trauma Dec 23 '14 at 19:20
• Simon, you misspelled its – James Waldby - jwpat7 Dec 23 '14 at 22:51
• @DigitalTrauma I think Physicist137's answer is better than anything I could come up with in that respect. – Simon B Dec 24 '14 at 8:39

Evolution. We are evolved to hear the sabertooth tiger getting ready to jump at us.

## What's "audible" is produced from what sounds commonly occur

There are many answers about why many things make a sound, but an important thing is that the the definition of "audible" - i.e., what wavelengths and power levels of mechanical vibrations fall within the "audible range" is a result of our environment. The proper answer to a question of "why interesting things fall within 20-20k hz" is that if there were common sounds relevant to our lives with, say, 15hz or 30khz frequency, then most likely our ears, brains and other organs would be slightly different and their hearing range would include 15hz or 30khz respectively.

why values in quiet are easily detected? A 60 dB dynamic range can be observed. In a quiet environment the hearing threshold is slightly above 0 dB. In the utmost tolerable sound environment, the threshold is 60 dB. Heerens & de Ru (Applying Physics Makes Auditory Sense, PDF here Direct copy & paste from here:

page 38 Chapter 4.

The role of DC signals in the organ of Corti and the cochlear amplifier

If we use realistic values for the various quantities we can calculate the extent of the
pressure effect on the basilar membrane. Deflections in the eardrum measure approximately
0.1 micrometer. For a deflection with a frequency of 1000 Hz, while the
density of the perilymph is estimated to be the same as that of water, 1000 kg/m^3 ,
and 1:1 is given for the amplitude amplification in the ossicular chain, the constant
pressure will be 0.1 mPa. This results in a factor of 5 above 0 dB SPL, which is
2×10^-5 Pa. If the amplification factor equals the estimated ‘pressure transduction’ in
the ossicular chain of approximately 25, the pressure load on the basilar membrane
increases by a factor 625, due to squaring. These values are easily detected, certainly
when sufficient resonance is present in the basilar membrane to evoke the required
signals in the auditory nerve.

• The system said: You must have 50 reputation to comment. So this answer is a comment, because I could not post it as a comment on the question neither the other answers, so I posted this here as an answer, but it is a comment. I do not have that 50 eputation. – Fall Apart Jan 4 '15 at 22:31

I would make three points to explain how you will almost always here sound when objects hit or brush together.

1. When two objects hit there will be an impulse over a very short time as one object speeds up or slows down. The Fourier transform of a very fast pulse is a very broad spectrum of frequencies. Therefore when two objects hit the energy spectrum will exist across an entire frequencies.

2. Any object will have some resonance frequency that will transmit sound energy fairly well. This frequency will depend on the object material and shape.

=>

1. When two object hit they will generate a wide spectrum of energy. Because any object will have some resonant frequency, some energy at that frequency will be transmitted. As long as an object will make sound at some frequency, it will emit sound when hit by a pulse.

Example. ( using antennas but the same principles apply )

If an antenna that is resonant at 100 MHz is driven with a very short electrical pulse, it will radiate energy at around 100 MHz for a very short time.

If a 500 MHz antenna is driven with that same pulse, it will radiate energy at 500 MHz for a very short time but not at 100 MHz. But it did radiate energy due to the pulse.

Therefore, hit any antenna with a pulse and it will radiate at its natural frequency. Hit any two objects together and they will emit sound around their natural resonances.

## protected by Qmechanic♦Dec 23 '14 at 22:44

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