I think I understand the difference between tempo ("speed of the track") and pitch ("sound frequencies used").
If we are dealing with only one sound frequency, would tempo and pitch be the same?
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It's hard to know exactly how to answer without knowing your background, but I think this should do it.
'Tempo' is how many beats per minute. The pitch is the frequency which is how many cycles per second. So they are similar sorts of concepts, both related to how many times something happens over a certain amount of time.
The tempo is the beat. Roughly speaking, if you were to clap along with a tune it would be how fast you were clapping. For instance, the tempo rating for the tune 'Stars and Stripes Forever' is listed at 'quarter note equals 120', which means 120 beats per minute. This also would be 2 beats per second. If a musician played the tune faster than normal, the pitches of the song would usually be the same, but the tempo would be faster.
The frequency gives the note you are listening to. For instance, the note A above middle C has a frequency of 440 Hz, or 440 cycles per second. The A one octave below that is 220 Hz. If a musician changes the note they were playing, (or if they go a little flat or sharp) they are changing the pitch to a different frequency.
If a track is sped up, both the tempo and the frequency will usually increase. But some software (like Auto-Tune) can apply some digital processing to change one without changing the other.
In music tempo does NOT refer to pitch, it refers to the time meter. We usually divide up music into a fixed number of "beats" per unit of time. We then denote the speed of the song by specifying the number of beats per minute at which we want the song played. For example 60, or 120. These are measures of bpm not Hz.
Now if you play a click track really fast you may perceive it as a low frequency "blurred" hum, but that is not its fundamental nature. Also, if you are trying to sample chunks of sound and decipher the presence of frequencies as well as periodicity of said frequencies then that may cause some of these concepts to get convoluted.
I am guessing at your intent because you are asking on a physics site rather than a music site. A percussive sound will usually have a lot of high frequency harmonics so one would want to look for that pattern over small time windows. Then looking for the presence of the same pattern "periodically" would help identify a tempo, or beat.
But to get back to the point, as musical terms these are completely unrelated.