Hearing is important.
You’ve likely heard from your mom, “Listen with your ears, not your
mouth.” Your spouse or some other wise guy
might’ve said this more than once during your less gracious moments.
One day your spouse drags you (by your ear no less) to the
doctor because of the exact problem above.
She claims you don’t pay attention when you should, don’t respond when
you should or speak when you shouldn’t. The
complaints vary in type and number, but you get the point. So your doctor, in order to dispel further
intra-marital distress and possibly save your marriage, may evaluate your
hearing.
Naturally, hearing requires one to receive and interpret
sound. But what exactly is sound? Ever think about that? I lie awake in bed pondering this stuff. Or maybe it was the coffee at 10 pm.
We’ll talk about how the ear receives and processes sound
and the different methods to test hearing in future posts. This article discusses the actual physics of
sound mechanics.
I know what you’re thinking: “Physics? Are you kidding me? Are you trying to lose your audience? Shoot me now!—it’s more merciful than
Death-By-Boredom!”
I’ll try to keep this simple and entertaining, though for
some folks, physics is synonymous with boring.
I personally find physics fascinating and far from boring, but I’ve been
told my mind functions in ways nature never intended.
So let’s get to it. A
beer or two usually enlivens topics of an academic bent. So instead of cringing, crack open an
ice-cold one.
Sound is created when something vibrates. The vibrating body (i.e, the source of the
sound) creates forces which in turn causes the medium around it to
vibrate. A medium is defined as any
intervening or surrounding substance through which a force acts. This requires the presence of molecules, tiny
particles of mass adjacent to one another.
Air is considered a medium since there are various molecules that
comprise air (oxygen, nitrogen, carbon dioxide and the like) much like a soup,
a really thin soup. Air is not just
empty space.
Sound moves by the vibration of molecules in a medium such
as air from one place to another. The
force created by the sound source is passed to the air molecules next to it,
causing them to vibrate. These vibrating
molecules then pass the force to other adjacent molecules, which in turn passes
it to their neighbors. This continues
until these vibrating forces ultimately strike the target, which in this case is
the ear.
Surprisingly, air is considered a liquid though it’s not as
dense a water. Yes, sound travels
through water. Whales and dolphins
communicate by transmitting sound through the ocean. Submarines use sonar (which utilize sound
waves through water) to locate objects around it. Sound also travels through bone, where
molecular forces are transmitted from various molecules that comprise bone. You can hear sound transmitted through your
skull, no matter how dense you’ve been told you it is. You can also hear sound transmitted through steel,
such as a railroad track, and by placing your ear on a track, you could hear an
approaching train that is miles away.
Sound cannot occur in a true vacuum, where there are no
molecules. There is no sound in outer
space. Us older folks might recall the ad
for the movie Alien in the 1970s.
The caption was, “No one can hear you scream in space.” This is true.
This topic might get a bit technical, but please bear with
me. The forces generated by the sound
source creates a phenomenon called pressure. Pressure is an abstract concept and is
defined as the total force over a given amount of surface area. The mathematical equation (for those physics
purists) is
Pressure = Force ÷ Surface
Area
Sound is created by a pressure wave that oscillates from the
sound source through the medium (we’ll use air in this case) to the ear drum (tympanic
membrane). A wave is a description
of this oscillation or vibration. A single
wave of sound consists of varying pressures, where on one extreme is a maximal
amount of pressure (the peak of the wave) and the other a minimal amount
of pressure (the trough of the wave).
These peaks and troughs are depicted in the Figure 1. In the middle of the wave is the resting
state, which we’ll abbreviate as P0 (P is used in physics as a
mathematical symbol for pressure, and the subscript “0” is—you guessed
it—"zero”). However in this case, P0
is not zero pressure. P0
is atmospheric pressure or the normal pressure all around us in a resting
state. If P0 was actually
zero, we’d be in a vacuum, a state where there are no air molecules. Again, sound cannot travel in a vacuum, and
we don’t live in a vacuum, though I’ve been told during my youth there exists
one between my ears.
 |
| Figure 1 |
O.K., let’s run through this with an example. Two physicists walk separately into a bar. Sir Isaac Newton arrived earlier and is sipping a beer when his pal Albert Einstein walks in. When sound is created, say when Sir
Isaac yells to Albert Einstein from afar, Isaac’s vocal cords vibrate. The
vibrations are then passed along to the molecules in the air surrounding his larynx
(“voice box”) in all directions. The
vibration creates an oscillating pressure wave, where at first pressure created
by the sound is greater than P0.
As the wave travels away from Isaac's larynx, the pressure decreases
until it is the same as P0, then decreases further so that it is
lower than P0. The pressure
then increases again reaching P0 and then increasing above it. The
wave travels repeatedly in this fashion, with peaks and troughs, over and over
again, (much like my 3-year-old son with his many questions back in the day) in
this cyclic fashion until it eventually reaches Albert’s ear. Think of sound as travelling in a repeated
crescendo/decrescendo pattern (i.e., up and down, up and down, etc., and keep
your mind out of the gutter).
Now that we’ve bludgeoned that topic to death, let’s move
on.
A wave has two important features: amplitude and wavelength. Amplitude is the height of the wave or
intensity of sound energy; the taller the amplitude, the greater the
intensity and the greater the loudness of the perceived sound. Wavelength is the total distance (in
fractions of a second) that one complete cycle travels. A cycle starts at P0 , increases to
reach its peak (the maximal height of the wave) where it crests and then
decreases, reaches P0 and decreases below P0 to its
lowest level (the trough of the wave).
After it hits the trough, it increases again towards P0. This journey is one complete cycle, as Figure
1 shows.
The number of wavelengths travelled in fixed amount of time
(one second) is termed frequency.
Frequency is the number of cycles per second, a cycle being one full
wavelength. As you can see in Figure
2, there is an inverse relationship between wavelength and frequency: the
longer the wavelength, the lower the frequency; the shorter the wavelength, the
higher the frequency. The speed of sound
is 767 MPH, which remains constant, no matter what the frequency or amplitude
of the travelling wave. So, if you
reduce the wavelength, you’ll have more waves in a particular stretch of
time. This increases the number of waves
that travel in a second and therefore increases the frequency. If you increase wavelength, you decrease
frequency. Frequency is also known as
“pitch.” So higher frequencies are the
same as higher pitches. Women, children
and a nice scratch on a chalkboard have higher frequencies (more treble sound
quality) compared to the voices of men, tenor singers, or that annoying
teenager with the booming subwoofer pounding from his car (more bass sound
quality).
 |
| Figure 2 |
The unit for frequency is Hertz (abbreviated
Hz). This is not the same Hertz
as the rental car company nor is it the type of pain you’re no doubt feeling at
this moment reading this post. One Hz is
equal to one cycle per second. So 4,000
cycles/second is the same as 4,000 Hz.
To summarize: sound requires molecules that are propagated
from the sound source to the target through the medium of air. This creates a pattern of vibrating or
oscillating pressure changes that travel to the target, and that target is your
ear. From there sound energy is received
by the ear, where it triggers a bunch of interesting physiologic stuff and then
delivered to and processed by the brain to create meaningful information. Well talk about this in the future.
Hopefully I haven’t lost or bored you to this point. How could a discussion featuring such chaps as
Newton and Einstein be boring? I’ll be
satisfied if you’re still awake and the beer you might’ve guzzled is the source
of your drowsiness. Now would be a good
time for a double expresso. Physics
tends to do this--that is, drain one’s energy.
No doubt, there’s a physics theorem or mathematical equation for such energy-sapping
activities interesting only to physicists and masochists, which we’ll not
endeavor to explore for the sake of death-by-boredom prevention. See you next time.
©Randall S. Fong, M.D.
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