user4003: If I record a sound at a rate of 8,000 samples per second, I know that the highest frequency that can be reproduced from the sound is 4000Hz. What I want to know is:
If the sound contains frequencies above 4000Hz, when I play the sound back what would I hear and what frequencies would be produced at the points where the frequency of the original sound is greater than 4000Hz.

user2569: The result of using a sampling rate that is too low for your program material is easiest understood with a graph.
If the blue wave is the actual sound you are attempting to record, in your example, say, 4.5KHz, with a sample rate of 8,000 samples/sec, the signal can only be recreated with the information that was recorded (in red).  So to answer your question, you get a lower frequency.


user3908: Sounds above the Nyquist limit (in this case 4000 Hz) will seem to fold back into the allowed range. For example, a tone 100 Hz above the limit will appear as a phantom tone 100 Hz below it. So a frequency of 4100 will seem to appear at 3900, one at 4200 will appear at 3800, and so on.
This is called 'aliasing' or 'folding'. The apparent 3900 tone is an alias for the 4100 tone. Since actual, complex sounds are composed of many frequencies, the audible effect is not as clean as theory describes it.

4003: <p>If I record a sound at a rate of 8,000 samples per second, I know that the highest frequency that can be reproduced from the sound is 4000Hz. What I want to know is:</p>

<p>If the sound contains frequencies above 4000Hz, when I play the sound back what would I hear and what frequencies would be produced at the points where the frequency of the original sound is greater than 4000Hz.</p>
 2569: <p>The result of using a sampling rate that is too low for your program material is easiest understood with a graph.</p>

<p>If the blue wave is the actual sound you are attempting to record, in your example, say, 4.5KHz, with a sample rate of 8,000 samples/sec, the signal can only be recreated with the information that was recorded (in red).  So to answer your question, you get a lower frequency.</p>

<p><img src="https://i.stack.imgur.com/B4hCQ.gif" alt="Nyquist Frequency"></p>
 3908: <p>Sounds above the Nyquist limit (in this case 4000 Hz) will seem to fold back into the allowed range. For example, a tone 100 Hz above the limit will appear as a phantom tone 100 Hz below it. So a frequency of 4100 will seem to appear at 3900, one at 4200 will appear at 3800, and so on.</p>

<p>This is called 'aliasing' or 'folding'. The apparent 3900 tone is an alias for the 4100 tone. Since actual, complex sounds are composed of many frequencies, the audible effect is not as clean as theory describes it.</p>
