A question about sound waves

How do we hear noises, such as eee and ahhh, differently? What is it about sound waves that allows us to hear a difference between such sounds of the same pitch and volume?
That question has been bugging me for ages :/

Have you heard of timbre? In musical terms it's "what gives a characteristic sound". In physical terms, however, it's a description of all the different sound waves which add up to make one composite wave. (Think: Fourier analysis)

For example, a violin approximately produces "sawtooth waves" which are a composition of many sine waves, which can have the same frequency as a pure sine wave (an electronic tone) or the same frequency as as really jumbled up mess of a wave (which is what I imagine speech looks like).

On top of that, sounds used in speech often change pitch. Consonant sounds are kinda a percussive sound followed by a vowel sound, so you also recognise stuff based on patterns like that.

Awesome, thanks How do you know this stuff, what were your sources? I ask because I'd like to look into it a bit more

For example, a violin approximately produces "sawtooth waves" which are a composition of many sine waves, which can have the same frequency as a pure sine wave (an electronic tone) or the same frequency as as really jumbled up mess of a wave (which is what I imagine speech looks like).

Not quite right.

Fourier is a mathematical model used to describe or synthesise complex waveforms by decomposing the waveform into discrete sine waves of varying amplitude and frequency.

Fourier analysis will only ever yield an approximation of the original (albeit an adequate for most practical purposes description) because perfect decomposition requires an infinite number of sine waves.

The production of a waveform does not require a source of sine waves. For instance, hitting a drum or an explosion creates a pressure wave followed by some kind of resonance from multiple sources. A square waveform can be produced by flipping a switch on and off.

Is the gist of what I said right? Because I was kind of guessing a little so confirmation would be good.

The square waves and whatever the drum wave is (I think I read somewhere that they were Bessel functions? Whatever the hell those are...) could both be considered to be a sum of sine waves, even though there actually aren't any. I'm not suggesting that humans literally work out the function that the want to produce, decompose it and then produce hundreds (or an infinity) of different amplitude sine-waves separately. Just that the process which afaik does take place reminds me a little of Fourier.

Yeah, you got the gist of it.

Fourier analysis is a mathematical tool which has really found application since the development of electronics and computing technology for both waveform analysis and waveform synthesis.

For instance, real-time analysis of a radar signal return to extract the Doppler frequency of a return echo and hence determine the velocity of an object being tracked. The return will comprise background clutter and definitely multiple objects all with shifting frequency returns which need to be extracted from the wideband noise.

Deep-space probe communications, autonomous guidance control, speech recognition software are some of the other applications.

Bessel functions are Eigenfunctions and are useful in revealing the spatial scale of transient functions by finding the bounded solution to a partial differential problem using an infinite sum of terms.

If you study signal processing at uni' you will cover these and more extensively.