# How to phrase the question of measuring the frequency of a complex sound?

I was hoping I could crowd source some understanding.

Im interested in understanding the measuring of sound pitch. From what I've been able to gather thus far- sounds are waves of air pressure and can be measured by a microphone (a tool which converts the vibrations of air waves into electrical energy). The signal recieved from a microphone represents the amount of air being displaced relative to the capacity for which the microphone can measure and the microphones resting state.

So from the information above, I can reasonably understand that if hypothetically something were to disturb the air in a given space, that the particles of air adjacent to the source would move away from the origin in a wave like pattern; assuming the microphone was in proximity and the air pressure generated was strong enough, the microphone would ouput an electrical analog signal; and that if something disturbed the air in a given space continually over a peroid of time then each disturbance would generate a set of particles which moved away in wave like patterns; Those sets of waves would reach the microphone in succession, each wave generating a signal within the microphone. The microphone signals could be recorded to show their change in value in relation to time. Given the time frame of a single second, if someone were to count all the waves that appeared in a sample they should be able to calculate the frequency of that sample.

So if my interpretation thus far is accurate then I should be able to construct the example that assuming there's a never ending vibrating string that creates a clean sine wave of the musical note 'A'(440hz) then subsequently, there would be disturbed sets of air partilces moving away from that string in wave like patterns at a rate of 440 sets of air particles per second. The displaced air would travel through space until it reached a microphone at which point, each wave would be converted into an electrical signal and then recorded. After the sound was recorded, someone should be able to observe the recordings and calculate the number of waves in a one second sample. They would find 440 waves and conclude that the pitch of the source was at 440hz and that the noise sounded like the musical note 'A'.

Alternatively, and here's where I think my understanding breaks down- if the sound is not clean or repeatitive in nature then how is the frequency (pitch) changed? How would a non uniform waveform sound in comparison to a uniform waveform when both samples have the same number of waves for a given second but look very geometrically different?

Also, determining the pitch of a sound whose duration is less than a second? Like a single drum beat and how the pitch would change as the number of drum beats increased into a seemingly continuous tone.

Thank you very much for your time and awareness. I highly appreciate any input.

• This is the most common misconception about sound: it's true that when you mix two colors, you get a different, single color. But if you mix two sound waves of different frequencies, the frequency isn't changed. You just have a wave with both frequencies in it at once. – knzhou May 14 '16 at 1:44
• If you want intuition for what the combined wave looks like, try this. – knzhou May 14 '16 at 1:44
• @knzhou That actually true for light as well (that you get a compound wave with both frequencies still present), but your visual system is insufficiently sophisticated to know the difference so it merrily lies to you. – dmckee --- ex-moderator kitten May 14 '16 at 2:43
• Vocabulary wise, you don't measure the frequency of a compound wave, you measure the spectrum: which set of frequencies are present and how strongly. In terms used to describe music you have overtones and harmonics; and you may get beats. – dmckee --- ex-moderator kitten May 14 '16 at 2:44
• Physics describes the way sound and light propagate, it can't say anything about how they sound and look like. That's a problem for human physiology and in your case psychoacoustics. Light and sound can be decomposed into Fourier components, but that's just a mathematical operation. For the purposes of physics it's an equivalence operation, time as well as frequency domain descriptions contain the same information. Sometimes, for simple mixtures of frequencies, the frequency domain representation makes it easier to interpret a wave, but it still won't tell us what it sounds like in detail. – CuriousOne May 14 '16 at 2:47