# Interpretation of sample rate

I'm a little confused about the sample rate:

If I have an audio file that was recorded with a sample rate of 48kHz, this means that there are 48,000 values per second in this file, right?

So when I read this file with a smaller sample rate of lets say 44.1 kHz I am summarizing every 44,100 values to one second so effectively I make the audio slower and thus longer than it actually is. Am I getting this correctly or do I have a total misunderstanding?

Yes that is correct-- if you sampled the audio recording at 48 KHz and then played those same samples back at 44.1 KHz you would be "time-stretching" the recording and it would be slower. However you can also resample the samples by the ratio of 147/160 to then have the 44.1KHz samples play back at the same speed.

That is correct. And You are basically interpolating the sampled signal at a slower rate. A frequency domain picture is that when you sampled at $$48khz$$, and assuming the maximum frequency component in the audio signal was no more than 2$$4Khz$$, then this $$24khz$$ component will get mapped to digital frequency $$\omega = \pi$$.

But when you play it back at sampling rate $$44.1Khz$$, then $$\omega = \pi$$ will get mapped back to frequency $$22.05Khz$$. This will result in high frequency tones sounding like low frequency one. A simple example will be that a high pitched woman's voice sounding like a low pitched male voice.

I always prefer this f-domain picture over t-domain picture.

You are right. If you play back your original samples at a lower sampling rate, the resulting signal will sound at a lower pitch, and will take longer to play.

If you want to convert your original samples to a lower sampling rate (but keeping pitch and length, and losing a bit of bandwidth), you need to resample your signal.

Most audio software, tools and libraries support resampling (to higher or lower rate).

You can read about the process (e.g. Wikipedia), but it generally consists of a combination of digital low-pass filtering, compression and expansion blocks.