My pet Sound question
December 2, 2011 1:39 PM   Subscribe

Despite taking several physics classes many years ago I don't think I understand how sound works. I was watching the excellent Behind the Sounds video about creating "Wouldn't It Be Nice" and thinking about how all those instruments at different registers ultimately are just recorded as one wave (in mono) or at most two (in stereo) that hit the ear. How can one wave carry such a density of information (like the Beach Boys) yet only carry information based on frequency, wave length and intensity? How can I tell that there are all these instruments when I only hear one wave?
posted by 2bucksplus to Science & Nature (14 answers total) 12 users marked this as a favorite
This article about Digital Audio might help you, especially the stuff about time domain vs. frequency domain and the Fourier Transform. We can differentiate instruments because our ears have fibers with very different resonant frequencies - essentially our ears can take a time-domain signal and perform a mechanical version of the Fourier transform on it. The signal that is sent to our brain contains information about each individual frequency.

On a more personal leve, the ability to "pick out" instruments on a recording is not an innate one - it's definitely a learned skill (although many people may learn it unconsciously).
posted by muddgirl at 1:58 PM on December 2, 2011 [1 favorite]

it's not just frequency, wavelength, and intensity. the waveform is the thing that tells us how a thing sounds.
posted by Jon_Evil at 2:12 PM on December 2, 2011

Maybe it would help to think about you perceive sound; everything you've heard in your entire life has been transmitted to your brain in the form of two waves; one from the eardrum of each ear. The physiology of your ear and brain does an amazing job of taking a single waveform that's everything you're hearing all mushed together into pressure changes in your ear canal and unpacking it into all the various sources of the distinct sounds.
posted by contraption at 2:14 PM on December 2, 2011 [1 favorite]

For what may be a somewhat conceptually simpler idea than Fourier transforms, check out the Wiki on Fourier Series. Here is a very rough overview:

An ideal wave, from a physicist's point of view, is just a sine wave. Why? Two reasons: 1) You can build up any function through linear combinations (sums and differences) of sine waves, 2) the math is relatively easy. So when you hear "sound is made up of sine waves," really what is meant is, "the easiest way we know how to mathematically describe how these things behave is through the use of sines and cosines."

So the "wave" can have a bunch of different peaks and valleys--information--but all of that can be encoded as partial amplitudes of various "fundamentals." You can imagine this as the effect of a bunch of overlapping waves.

A very good analogy (conceptually and mathematically, as it turns out) is to cardinal map directions. Using north, east, south, and west does not limit you to only describing directions that are purely along those axes. You can very well say, "Go north 1 mile and east 3 miles," or whatever.
posted by dsword at 2:33 PM on December 2, 2011

Here is your answer.
posted by empath at 2:37 PM on December 2, 2011 [4 favorites]

There are two parts to this -- the physics, and your ability to understand it. I don't know much about the latter, so I'll leave that alone (although you might be interested in googling Diana Deutsch's work on how people process sound), but I'll take a stab at the physics part:

Basically, it IS just once signal -- but it's not a wave in the nice, clean sinusoidal sense, because what you have is a combination of the waves produced by all the instruments, and their respective envelopes. There's a lot of information there.

Let's say you've got a perfect concert A, produced not by an instrument, but by a machine, like the beep on old computers. It's an air pressure wave, and if you picked it up with a microphone and looked at it on an oscilloscope, you'd see a nice clean sine wave that corresponds to the air pressure at a function of time; concert A oscillates at 440 beats/second. Lower the pitch, and that sine wave gets wider; raise it, and it gets tighter -- frequency=pitch. Raise the volume, and the amplitude gets bigger (the wave gets taller) but the frequency stays the same -- amplitude=volume. Changes in the volume form an envelope containing the wave, and how that envelope is shaped is what you will perceive as the attack or the dynamics. An explosive sound has a huge amplitude starting from nothing, a crescendo will slowly increase, and a hum will start small, grow taller, and shrink again. (That's partly why speech played backward sounds funny -- most speech starts loud and diminishes as we run out of air, and played backwards the envelope's reversed.) When you listen, you're detecting two independent channels in the wave -- pitch and volume -- plus how both vary in time.

With music, you have all of these notes -- different waves with different envelopes surrounding them. And if we have two at once? Those waves add up, so that you're now not looking at pure sine waves inside an envelope, but the sum of them. If the frequencies of the waves you're adding aren't multiples of each other, the amplitude will warble a little over the duration of the sound simply due to the addition of the two notes. That slight, rapid oscillation in amplitude is something you'll hear either as an unpleasant dissonance or a pleasing harmony, and hearing the beat frequency is part of your ability to perceive that there are multiple voices.

On top of that, even a single instrument will have harmonics; the instrument itself rings a little, so that you don't ONLY get 440 when you play an A. The particular way an instrument rings depends very delicately on its physical construction, which is why you can tell a Steinway from a Yamaha, even though both are pianos: Yamahas resonate a bit more at higher harmonics (ie, there's a little bit more 880, 1760, &c. mixed into the Yamaha's A than there would be on the Steinway), making them sound "brighter." It's even more pronounced with people's voices, which is how you know who's singing.

Moreover, the waves from real instruments aren't necessarily smoothly sinusoidal. For example, you know how if you turn up the volume too loud on a cheap stereo it sounds "clipped"? That's the top of the waves being flattened, and it'll sound qualitatively different from an amp that isn't clipping. Imperfections like that, too, are part of the information that the waveform contains -- and hence part of what you hear and understand to be, eg, the characteristically overdriven awesomeness of rock and roll electric guitar!!! \m/ \m/
posted by Westringia F. at 2:47 PM on December 2, 2011 [3 favorites]

It's useless to look at a waveform and imagine what sound your eyes are seeing. Kind of like putting your ear up to a painting.

But just for comparison, you won't have any problem visually discerning layers, for instance, here.
posted by StickyCarpet at 3:18 PM on December 2, 2011

Your ear can add sounds together by itself. It can hear a guitar pluck and a piano note and be able to tell when a sound is comprised of the two of them in unison.

The ear is also highly suggestible.
posted by rhizome at 4:11 PM on December 2, 2011

Err... by "your ability to understand it" I meant the ability to interpret the sound as music, not your ability to understand physics! That was never in question :)
posted by Westringia F. at 4:16 PM on December 2, 2011

The study of how we perceive and seperate sounds is known as Auditory Scene Analysis coined by Albert Bregman who had this analogy -

Your friend digs two narrow channels up from the side of a lake. Each is a
few feet long and a few inches wide and they are spaced a few feet apart.
Halfway up each one, your friend stretches a handkerchief and fastens it to
the sides of the channel. As the waves reach the side of the lake they travel up
the channels and cause the two handkerchiefs to go into motion. You are
allowed to look only at the handkerchiefs and from their motions to answer a
series of questions: How many boats are there on the lake and where are
they? Which is the most powerful one? Which one is closer? Is the wind
blowing? Has any large object been dropped suddenly into the lake?

It's a fascinating subject!
posted by TwoWordReview at 6:13 PM on December 2, 2011 [1 favorite]

Your eardrum is just one membrane that vibrates based on the sound waves that run into it. They can come from all different directions, but they end up as a single waveform.
posted by gjc at 8:26 PM on December 2, 2011

Maybe it would help to think about you perceive sound; everything you've heard in your entire life has been transmitted to your brain in the form of two waves; one from the eardrum of each ear.

You don't only hear through the ear. Resonant cavities in the head and body vibrate and can detect directionality, albeit more crudely than the ear does. It's all cumulative. This is like saying you only taste with your tongue.

People also hear through their eyes and, most of all, through their brain. So much of what is heard is determined through other means. Yes, much of it has nothing to do with sound as such.
posted by Wolof at 5:28 AM on December 3, 2011

How can I tell that there are all these instruments when I only hear one wave?

Because in an elastic medium such as air, all the little waves coming from every part of each instrument add linearly, forming a composite wave that carries contributions from all of them, and it's that complicated, irregularly-shaped composite wave that gets represented on the recording.
posted by flabdablet at 7:32 AM on December 3, 2011

Another short answer: because sound waves can carry a lot more information than it might seem if you are just thinking of them as sine waves.

Thought experiment: picture yourself at the ocean. The wind is low that day, and the waves coming on shore are just little swells that show up on shore. Next, you set up an apparatus that drops water at a regular rate to form little wave patterns like this. You will see those tiny waves riding along with the lower amplitude swells. (Which are riding on top of the really lower amplitude tide.)

If you stuck a ruler into the sand and were able to measure the height of the water very quickly, you would be able to see all the different waves. The height would change slowly over time, because of the tide. It would also change more quickly because of the swells, and then really quickly because of the droplets. Each one sort of rides on top of the other one. Their amplitudes interact with each other, but their frequencies are still there.
posted by gjc at 9:09 AM on December 3, 2011

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