Electrical/mechanical representation of instruments and space


Help, I'm stuck at the juncture of physics, mechanics, electricity, psycho-acoustics, and the magic of music.

I understand that the distinctive sound of a note played by an instrument consists of a fundamental frequency plus a particular combination of overtones in varying amplitudes and the combination can be graphed as a particular, nuanced  two-dimensional waveform shape.  Then you add a second instrument playing, say, a third above the note of the other instrument, and it's unique waveform shape represents that instrument's sound.  When I'm in the room with both instruments, I hear two instruments because my ear (rather two ears, separated by the width of my head) can discern that there are two sound sources.  But let's think about recording those sounds with a single microphone.  The microphone's diaphragm moves and converts changes in air pressure to an electrical signal.  The microphone is hearing a single set of air pressure changes, consisting of a single, combined wave from both instruments.  And the air pressure changes occur in two domains, frequency and amplitude (sure, it's a very complicated interaction, but still capable of being graphed in two dimensions). Now we record the sound, converting it to electrical energy, stored in some analog or digital format.  Next, we play it back, converting the stored information to electrical and then mechanical energy, manipulating the air pressure in my listening room (let's play it in mono from a single full-range speaker for simplicity).  How can a single waveform, emanating from a single point source, convey the sound of two instruments, maybe even in a convincing 3D space?  The speaker conveys amplitude and frequency only, right?  So, what is it about amplitude or frequency that carries spatial information for two instruments/sound sources?  And of course, that is the simplest example I can design.  How does a single mechanical system, transmitting only variations in amplitude and frequency, convey an entire orchestra and choir as separate sound sources, each with it's unique tonal character?  And then add to that the waveforms of reflected sounds that create a sense of space and position for each of the many sound sources?

77jovian
I think it’s an excellent question and actually a question that has a whole lot to do with the questions I’ve been asking on another thread: What is the audio signal in the system prior to the point where the speakers produce the acoustic waveform of the entire orchestra? AND how do better speaker cables, better power cords better fuses, vibration isolation affect the “audio signal,” whatever it is.
The microphone acts no different than your ear drum or speaker cone. How a single cone produces overtones is simple. Say you are listening to a 20 hz tone. The speaker cone moves back and forth 20 times a second. For a 100 hz tone it’s a hundred times a second.

What about the two tones played at the same time to produce a different sound? As the cone moves forward 20 times per second, it also moves back and forth 100 times per second. (Wave your hand back and forth with your arm still. Then move your arm while your are waving your hand. Then walk forward while waving your hand and moving your arm. The air displaced is a pressure representation of the combined motion).

The combination of pressure waves creates one wave at any point in time and over a certain time period it contains all the other waves (overtones) creating a particular sound. Add them all together as a function of time and there is your orchestra in your living room.
A few things to consider here:

  1. You get placement information of instruments via two methods, volume and timing. If the right side is louder for a particular instrument, then that is where you perceive the instrument is coming from. That is the mechanism for placement of sounds that are continuous. The other mechanism is arrival time (between the left and right ear). That is used for transient sounds. A clap will arrive to one ear slightly before the other. Your auditory processing system is able to time that to pretty fine resolution and give you an idea of where it came from. Some posit that arrival time also plays a factor in placement of continuous sounds.
  2. The electromechanical system only stores and transmits sound waves (pressure variation). It does not transmit instruments, etc. It is your brain, knowing what a grouping of sounds mean, that is able to extract instruments and place them.
A single speaker will not convey on its own, any sense of space, but a room may create those cues (accurate or not), and your brain doesn't like an information vacuum so it will try to map what it hears onto what it knows.

I think you meant frequency and time domain. Amplitude is part of either frequency or time domain.
77jovian commits an all too common flaw in logic which since no one studied logic no one caught. Except me, of course.

Hint: "two ears"-
When I'm in the room with both instruments, I hear two instruments because my ear (rather two ears, separated by the width of my head)

Two ears. Got it?

Then, inexplicably:
But let's think about recording those sounds with a single microphone.

Wait- what?!?! 

Need I say more? Really?

Yeah, yeah. I could answer the one mic question too. But fix the first one first, okay?
Um, first, some instruments don't have a lot of energy in the fundamental.

But otherwise, you may be very interested in Head Related Transfer Functions.

Best,
E