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I have a 440 Hz tuning fork (Pure Frequencies brand, aluminum) that I use for simple acoustics experiments. When I strike it more than once in quick succession, the pitch I measure seems to shift by 1–2 Hz compared to a single clean strike. I've read that temperature changes can slightly affect a tuning fork's resonant frequency, since the elastic modulus and dimensions of the metal change a bit with heat — so I suspect hand contact or repeated striking might be warming the tines just enough to cause this. So far I've tried: striking with a rubber mallet instead of my hand to reduce heat transfer (drift got smaller but didn't disappear), letting the fork cool to room temperature between strikes (more consistent readings), and testing a second, different-brand fork (saw a similar but smaller effect). Is this drift consistent with thermal effects, or could it be a measurement artifact (e.g., beats from overlapping decay tails)? Is 1–2 Hz within normal tolerance for a fork like this?

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  • $\begingroup$ How do you measure the frequency, and what is the precision you can get from your measurement device? $\endgroup$ Commented 22 hours ago
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    $\begingroup$ You also didn't mention the value of ambient temperature when you measured the pitch. $\endgroup$ Commented 21 hours ago
  • $\begingroup$ Can you measure the (single strike) frequency as a function of ambient temperature and see how big the variation is? If the frequency change per degree is much less than 1-2 Hz that makes it improbable that temperature changes are responsible for the effect you see. $\endgroup$ Commented 21 hours ago
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    $\begingroup$ it could be beatings... but the first thing to look at is the spectrum of the fork - perhaps, its width is a few Hertz already - see, e.g., here $\endgroup$ Commented 18 hours ago
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    $\begingroup$ There are psychoacoustic effects where transient overtones can make the fundamental pitch appear to shift when it does not — guitar strings do this. Can you share a recording and/or a spectrogram? A nice tool (for many things!) is the Physics Phone Experiments (phyphox) app. On a bigger computer there are lots of options for making spectrograms, such as Audacity. $\endgroup$ Commented 12 hours ago

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Some quick estimates suggest thermal expansion is not enough to account for a 1 part in 400 change of frequency. You might consider issues such as how the tuning fork has been handled, whether it could have picked up some moisture which then evaporates, and things like that. To get better answers you should probably do a more controlled experiment. The evidence presented in the question is a bit vague. Does the frequency go up or down if the fork is struck twice in succession? What is the experimental uncertainty on each frequency measurement? What is the variation observed in multiple measurements? Is the effect certainly there?

To test all this you might perform, say, 100 measurements in a row, some with 60 second gaps between measurements and some with 1 second gaps between measurements, and then do statistical analysis on the results.

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Based on the information in the question, a decrease in pitch of $1$-$2$ Hz is realistic. However, a careful assessment of the expected value is not possible without additional information on ambient temperature, some control on the fork temperature, and the exact composition of the aluminum tuning fork (usually, it is some aluminum-based alloy)

According to Wikipedia, the frequency $f$ of a tuning fork depends on the size, density, and Young's elastic modulus $E$ of the fork according to the following formula: $$ f=\frac{\alpha^2}{2 \pi L^2}\sqrt{\frac{E I}{\rho A}},\tag{1} $$ where $\alpha$ is a numerical constant ($\sim 1.875$),$L$ is the length of the prongs, $I$ is the second moment of area of the cross section, $\rho$ is the density of the fork's material, and $A$ is the cross-sectional area of the prongs. All the geometric quantities and the density depend on temperature. However, the size and density vary by a few orders of magnitude less than Young's elastic modulus at normal temperature. Indeed, a typical value for the linear expansion coefficient of aluminum alloys is $\sim 2~10^{-5}$ K$^{-1}$.

Available literature data allow us to estimate a rough figure of about $1$% for the relative variation of Young's modulus ($E$) in response to a temperature change of $10$ K ($E$ decreases as temperature increases), which dominates the temperature effect in the formula ($1$). Therefore, a decrease in frequency by $1$-$2$ Hz is a reasonable estimate for tuning forks vibrating in the range $400-500$ Hz.

Moreover, it is consistent with the fit of measurements contained in this paper if the increase of the tuning fork temperature is of the order of about $10$ K.

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    $\begingroup$ ... so, since the temperature change is nowhere near as large as 10K, your argument implies the Young's modulus is not the culprit. Some deformation of the tines, whether thermal expansion or another cause, is probably worth considering. $\endgroup$ Commented 15 hours ago
  • $\begingroup$ @AndrewSteane I do not understand how you get this conclusion. A change of 1% in the Young's modulus would imply a change of 0.5% in the frequency. A tuning fork for central A (440 Hz) would decrease its pitch by about 2 Hz. In the required range. $\endgroup$ Commented 14 hours ago
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    $\begingroup$ @GiorgioP-DoomsdayClockIsAt-85 I'm skeptical tuning forks get that much warmer from being struck. A 0.5kg aluminum tuning fork requires about 4500J of energy to increase in temperature by 10 degrees - to achieve this, you'd need to smack the fork against something at about 300mph and have 100% of the energy turn into heat. $\endgroup$ Commented 14 hours ago
  • $\begingroup$ @NuclearHoagie. Normal steel tuning forks have masses of about 30 g. Aluminum tuning forks should be at least a factor $1/3$ lighter. Moreover, the heating effect is not kinetic; it is caused by handling a good thermal conductor at room-temperature, with human hands (at body temperature) $\endgroup$ Commented 13 hours ago
  • $\begingroup$ @AndrewSteane I have expanded my answer, providing more information and numbers that show the dominance of the Young's modulus variation with the temperature over geometric variations. $\endgroup$ Commented 13 hours ago
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When a tuning fork is resonating, the tines are moving in equal and opposite directions . It takes some time after the tuning fork is struck to achieve this state. If a tuning fork is struck repeatedly before the resonant state is reached (most people strike a single tine to activate the tuning fork) the tines are not in sync so the resonant frequency is not achieved and the measured frequency could be higher or lower. So the rate that the tuning fork is repeatedly struck affects the measured frequency.

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A tuning fork exhibits a phenomenon called simple harmonic motion, where the acceleration is proportional and opposite to displacement. In an ideal SHM system, the frequency is independent of amplitude, as explained by this article

A larger amplitude means the object travels further in each cycle — but it also moves faster (because it starts from a higher PE, converting more to KE). These two effects exactly cancel: larger distance but proportionally higher speed gives the same period.

In many real world examples of SHM, the relationship between acceleration and displacement deviates from ideal at large amplitudes, for a variety of reasons. This affects the frequency, as indicated by this qualifier from the above article:

This amplitude-independence is a defining property of SHM and does not hold for large-angle pendulums or nonlinear oscillators.

This effect is noticeable with a guitar, where the pitch of a string directly after plucking is significantly different to the rest of the note. It might also be the effect that you are observing when you strike the tuning fork repeatedly, as the amplitude might exceed the range for ideal behaviour.

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