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I bought a cheap tuning fork A 440 Hz. I measured its frequency to be 440.9 Hz. Since I bought it just for fun, not that I needed a precise frequency reference, I decided to screw around and to try to lower the frequency a bit.

After some research I found out that one needs to remove some material from the "crotch" of the tuning fork in order to lower the frequency. I did a few passes with a file over the "crotch" of the said tuning fork, and lowered the frequency down to 440.2 Hz.

Up to this point I measured the frequency using an instrument tuning app on my smartphone. I had checked its accuracy beforehand by playing an audio tone generated by a lab signal generator externaly referenced by a rubidium frequency standard. It turned out the app was quite accurate, it was spot on with precission of 0.1 Hz in that range.

After a week or so after filing the tuning fork, I gained access to the aformentioned signal generator, and wanted to accurately tune the fork to 440.0 Hz (just for the hell of it). Since I didn't have a frequency counter at hand, I used the said generator, an oscilloscope and a microphone to compare the frequencies according to Lissajous figures on the scope.

It is difficult to work out the possible error of the measurements. Stability of reference frequency of the wave generator is 1 ppm. The measurements were repeated multiple times, at least 10 times for each measurement. It is quite difficult to get spot on frequency by using Lissajous figure method. I have to hit the tuning fork before each measurement and I only get 2-3 seconds of clear image before the oscillations become to weak for a microphone to pick up. However, I can clearly see the limits when the frequencies are really off and that is within 1 Hz.

It turned out that the frequency of the tuning fork had drifted down to approx. 437 Hz by that time. At first I suspected that the frequency drift was due to the temperature difference. Further experimentation showed that temperature variation changed the frequency within the limits of 1 Hz (the frequency of the tuning fork was measured after keeping it in a freezer for an hour, and then the measurement repeated after keeping it immersed in boiling water for a while).

After a couple of hours the frequency of the tuning fork drifted to 435 Hz 😲. By the end of the working day it measured 432 - 433 Hz, and the next morning it was 431 Hz. It continued to drift only when using it.

My question was - what happenned? I remember reading somewhere, that after filing the middle section of the tuning fork it might take some time until the frequency settles, because of internal stress of the metal, but could it be that much?

Long story short - there was a crack in the tuning fork, right in the middle, which progressed when the fork was vibrating.

I first noticed after filing that there is brass solder on the "crotch" of the tuning fork (the fork was chrome-plated). There is no need for it to be there, so I initially thought that the one who was brazing the handle to the fork was not very careful with flame/solder/flux. Later while experimenting I heard an additional higher pitched tone in the sound of the fork, which was definitely not a harmonic of the fundamental. Upon closer inspection, I noticed a short crack. Moreover, I noticed that there were two "blobs" of solder at the crotch - one going all around the rod, and another on top of that for the handle. It seems that the rod was cracked during the bending (probably over-bent and then bent back), and the crack was brazed over. I opened the crack by filing off the solder and it progressed as the fork was used.

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    $\begingroup$ at each test condition, how many sequential measurements did you make? what was the mean and std. dev. of those measurements? $\endgroup$ – niels nielsen Nov 27 '19 at 7:19
  • $\begingroup$ This doesn't help your thread but i just wanted to say that i think this was a super fun experiment! Excellent use of time in my opinion :) I'm ordering one asap. (also musician so why not get one) $\endgroup$ – DakkVader Nov 29 '19 at 7:59
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Here are some things for you to think about.

First, to reduce the resonant frequency of a metal tuning fork requires the removal of enough metal from the crotch of the fork so as to significantly increase the effective length of the tines. It is highly doubtful that you did that with just a couple of passes of a metal file.

Second, to get a reliable result from a measurement tool requires you to know the repeatability of the tool i.e., if you measure the exact same thing with it 10 times in a row, do you get the exact same result on each of the ten trials? Or are there some slight random variations within the series of measurements?

I am guessing that all your different frequency measurements were due to slight test-to-test variability of the measurement tool, and what you need to do is run 10 trials at each condition and take the mean and standard deviation of those ten measurements- and THEN you compare the MEANS.

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  • $\begingroup$ I would look for measurement errors if I had 2-3 Hz deviation. What I have is in order of 10 Hz. Verified by recording a sound sample in the PC and calculating FFT, and also by a smartphone app. $\endgroup$ – Shariukas Nov 27 '19 at 13:47

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