How do you hear multiple frequencies at once?

Question

Say you are playing music through a speaker. You play a single note and the speaker responds to that one frequency. Now, if you play two notes together, the speaker alone produces what appears to be both sounds in unison although the speaker has a single cone generating the waves. Obviously, the cone cannot vibrate at two different speeds at once. I assume the same thing happens when sound hits your eardrums but what I'm really wondering is how a speaker (or eardrum) combines multiple frequencies so that they are all audible. And if I'm not hearing each individual pitch, then what am i hearing?

Answer 1

The speaker produces what is called a complex wave. There is only one cone position and only one instantaneous sound pressure level at any given time. But Joseph Fourier showed that a complex (periodic) wave can be expressed as the sum of pure sinusoidal waves. When we hear these complex waves, the ear can identify these sinusoidal components and it sounds like many frequencies at once.

In the picture here http://img182.imageshack.us/img182/6198/wavesyc8.png
the dark-line wave will sound as if it is two tones played together.

It is convenient in the description of complex waves to assume that they are the sum of the Fourier components, but we should not lose sight of the fact that there really is only one wave. When a complex wave is produced by a musical instrument, we hear mainly the basic frequency (tone) and identify the pitch with that. However, there are other frequencies that combine to produce the characteristic sound (tone quality) of that instrument. These are called "overtones", and we cannot usually identify them by ear individually.

Answer 2

The cochlea in your ear is a very clever structure. It is a narrowing spiral that operates in such a way that as sound travels through it the higher frequencies are progressively attenuated - ie they get queiter. So only low frequencies get to the far end, but lots of high frequencies are still about at the near end. Hairs along the cochlea pick up the vibrations of the sound and can tell how loud it is. Coupled with the progressive frequency attenuation the brain can then work out the level of different frequencies at the same time.

Answer 3

Yes, the loudness and tone (sharp, dull etc) correspond to the loudness and frequency.

We can also hear the shape of the wave - We can distinguish the same frequency from the drum or a flute.

When you mix two or more frequencies, you get a wave which is complex and varying in frequency. The speaker can produce the complex waveshape.

Answer 4

Simplifying the first explanation, the "haris" in your inner ear respond to the various component frequencies. For instance, when you hear a C-major chord, one set of receptors responds to the C, another to the E, and a third to the G. Your brain interprets these as three separate tones.

In case you know the terms -- each inner-ear "hair" is essentially a narrow-range band-pass filter.

Answer 5

maybe that because of hearing sensation....