Finding correct speed for track from converted tape

Hello
I am converting to digital some old tapes with music recorded from the radio with different tape recorders and often with wrong speed.
I have some music with people talking and often the songs are mixed with fade, so it is not easy to get the lenght.

So, after recording the tape with Audacity, till now I find the right speed by playing on another device the same song found on line, and trying to change and align on Audacity the track speed until they sound with similar speed. (Effect/Change Speed)
As you can imagine this (primitive) procedure takes a lot a lot of time.
Can you suggest me a more advanced way to find the correct speed ? I don’t need an extreme precision.
Many thanks
Mike

I don’t know of any way to automate it, but standard tape speeds are all a factor of two.

If the recordings have mains-hum (50/60Hz & harmonics thereof) you could use that as a reference, (see the spectrogram).
If the speed varies throughout you need something like Celemony’s Capstan.

the Trebor’s solution with harmonics seems very interesting (no wow and flutter) just different speeds depending on the recorder used on each track.
I’m trying to understand how it works, I have selected the range from 30 to 200 Hz looking for traces of harmonics or subarmonics of my 50 hz power. (see attachment)
I need to make some tests to better understand, but the suggestion looks good
Thank you

Need to increase the spectrogram FFT “window size” to 8192 or higher to see detail in low frequencies like 50/60Hz.

Can also use Audacity’s frequency-analysis plot … https://manual.audacityteam.org/man/plot_spectrum.html

Many thanks Trebor, sorry for late answer
increasing the window size gave me amazing results…
The 50 HZ note is quite wide it goes from 40 Hz to 60 Hz but, there are some harmonics around 85Hz and 125 Hz that are multiples of 42 Hz
So this shows, I am not wrong, that the track has slow speed and must be increased.
Just one thing is not clear, I cannot explain the presence of the harmonic at 150 Hz it seems stronger than the 85 and 125 Hz.
This could mean that the speed is ok and 85 and 125 are traces of a previous recording, on another device, not completely erased??

I am going to study the frequency-analysis plot as you suggested
Many thanks again Trebor for this incredible trick…

When the tape was digitized, new mains hum can be added during the playback which is not shifted.
So what you have in the digital audio can be a mixture of constant mains hum (& harmonics) at the correct frequencies,
plus the mains hum recorded on the tape which is not at the correct frequency if the tape was not played back at the correct speed.

NB: any tape speed-shift may not be constant throughout the recording.