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If I record something that is at 500Hz audio frequency then the sampling frequency will still be 44.1Hz. How does the 500Hz audio frequency fits with 44.1KHz sampling frequency? If the sampling frequency were 500Hz, would the size of file will be smaller? If yes, then why do we use sampling frequency?

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Similar to avp.stackexchange.com/q/3312/126 –  Friend Of George Mar 14 '12 at 12:50
the key to the answers here so far is that the term (Hz) is "cycles per second," but the term "cycle" refers to a completely different thing. –  horatio Mar 15 '12 at 13:56
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2 Answers 2

Well, it seems like you have to forget everything you know about sampling frequency and frequencies in general.

The frequency in terms of audio is the number of times the speaker membrane moves in and out per second. What makes it vibrate is that the power that is sent through the audio cable makes electromagnetism that pushes and pulls to the magnet inside the speaker.

Thus, the sound wave we are speaking of is going like a curve up and down. Let's say this was a perfect sine wave:

             _               _
           /   \           /   \
\         /     \         /     \
  \     /         \     /         \
   \ _ /           \ _ /           \

Say this is a pretty low frequency in terms of audio. If you use a low sampling rate to sample that it will be like this: (I've "sampled" the first 2/3 of the sound.)

 |   |   |   |   |   |       _
 |   |   | / | \ |   |     /   \
\|   |   |/  |  \|   |    /     \
 |\  |  /|   |   |\  |  /         \
 | \ | / |   |   | \ | /           \

This will result in a wave almost the same as the original one: (Here I've marked all the sampled points that we draw a line between. The mark is this: | This new line represents the sampled digital version of the analog signal that we started with.)

               |               _
             /   \           /   \
 \          /     \         /     \
   \     /          \     /         \
    \ | /            \ | /           \

If we use a high frequency sine wave it will look like this:

     |       _       |       _       |
     |     /   \     |     /   \     |
\    |    /     \    |    /     \    |
  \  |  /         \  |  /         \  |
   \ | /           \ | /           \ |

In this instance we sample only at the bottom of the curves. This leads to a wave that looks like this:



The higher the sampling frequency the more often you sample where the curve is. And as you see with the high pitched sound, it only samples at the bottom of the curve. Then it draws a line between the different sampled points and you get a flat line.

On the low pitched sound you can see that it samples the bottom, the middle and the top of the wave. If you draw a line through these points you will get a line that is almost the same.

If you use 44.1 kHz it will be able to reproduce everything from 0 Hz (20 Hz) to 20 000 Hz, which is what we are able to hear. If you use a higher, like for example the 48 kHz you would be able to sample higher frequencies than you could actually hear. Though to the good ear there will be a difference, maybe because the high frequencies affects the other frequencies.

So there you have it! Tell me in the comments if there is something you didn't understand.

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I guess so the number of times speaker membrane moves up and down depends on bitrate per second rather than frequency? For example: Can I assume a 128kbps audio file would produce 128000 approx. vibrations per second? –  user103241 Mar 14 '12 at 9:45
Also, I noticed when I change the sampling rate from lower to a higher frequency, audio data size and bitrate increases. E.g. If I convert 44.1KHz to 192KHz. Does the information size really increases or is it filled with null samples? –  user103241 Mar 14 '12 at 9:52
Ahh, forget what you know. It is two completely different things. The audio frequency is the rate at which the membrane moves out and in –  Friend of Kim Mar 14 '12 at 10:28
The sampling frequency is the rate at which the computer saves the value of the wave. –  Friend of Kim Mar 14 '12 at 10:28
Look at this: youtube.com/watch?v=zC5KFnSUPNo It is a video of what I just explained.. –  Friend of Kim Mar 14 '12 at 10:30
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Not sure I like the reference only to a speaker.

Frequency is expressed in cycles per second, also expressed in Hertz. A good example, "A" 440 is a standard pitch that is used to calibrate and tune orchestra instruments, it is the A above middle C, aka A4. If this was a pure sine wave it would vibrate at 440 times per second.

Let's simplify sampling.

If you have a painting that measures 40 feet across (think of something like Monet's Waterlilies) and I want to find out what it looks like by only seeing parts of it, how many slices would I need to recognize it?

40 feet at a sample rate like 44Khz, might be like .01 resolution, .01 x 40 = .04 or about a slice every 1/2 inch. Surely you would see what is going on in the painting if I showed you what every 1/2 inch looked like.

So applied to A 440 sampled at 44 Khz, I would be sampling a 440 cycles per second wave 44,000 times a second, and get a .01 resolution. I would be hearing it pretty good.

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