Using the mirror for the close up is just delightful.

That's a really smart use of the mirror

I study musicology, and I might be able to explain why we hear the mentioned phenomenon. The problem is both phenomenological and physical. Tuning forks are typically thickened at centre of their bent where the prongs meet the stem. When a tuning fork vibrates, the stem generates a vibration in a vertical direction that can be communicated to a table, or preferably, to a resonance chamber. Now, if you press your tuning fork to a table/resonance chamber, you change the fundamental tone, and you'll recognise the overtone which is an octave higher as the fundamental; nevertheless, if the thickness of the centre is not sufficient, this effect will be eliminated. Also, I think you can probably eliminate the effect by inclining the prongs towards each other. In fact, if you make tuning forks of various shapes, you will hear different pitches (other than an octave higher) when you press the fork against a table. In conclusion, what you need to pay attention to is the thickness of the stem and how the prongs are paralleled to one another. If you pay attention closely, you might also notice that the shape of the centre (where the stem meets the prongs) are different in circular tuning forks and square ones-the square tuning forks tend to have a more continuous/flat connection at the centre. That can also be a contributor to what I just explained. In summary, the octave effect is always present, but we can only hear it if the conditions are set for it:)

The mention of harmonics and guitars got me excited. There's this great effect you can do with guitars where you reeeeaaaallly lightly touch the string at points that correspond to nice logarithms. Because you are only touching very lightly, you aren't actually shortening the vibrating length of the string. Instead, you are trying to fix one specific point somewhere in the middle of the string, thus eliminating all of the harmonics of that string which do not have a node at that point. It ends up sounding like a totally different note, a perfect illustration of how harmonics are hiding inside what we hear. Also leads to a really interesting discussion on how the chords we find pleasant, and indeed our way of dividing an octave into 12 logarithmic semitone steps, are attempts to approximate whole number ratios of a base frequency.

Could it be that a tuning fork with a circular cross section has a steady state mode where the end moves in a horizontal circle without any up/down motion. That would be consistent with the frequency doubled peak decaying because the up/down motion decays, or energy is transferred to the horizontal circle mode. A tuning fork with a square cross section would probably not be stable in a horizontal circle mode.

i would kill to see one of those internal stress images in super slow motion for a tuning fork

Thanks for showing the shapes at 0:48 I couldn't remember what squares and circles look like without it

The silver one didn't appear to have a flat base so it probably just made less contact with the tables surface, and then had less of an effect.

So as a professional music theorist, I just wanted to drop in and say that the way you used the word "note" is entirely fine. While it can certainly be used to refer to pitch classes, as your detractors claimed, it's also fairly common to use it to refer to specific pitches. Middle C, for instance, is a note, and it's a different note from High C, despite the two being in the same pitch class. (C, to be clear.) Also, on this part of the question I think it might be worth re-examining harmonics a bit. If you look at the spectrums for the two 522 forks Hugh used, the rounded fork seems to have a much weaker second harmonic than the square fork. (the fundamental's a bit quieter too, but not by as much.) That initial set of frequencies doesn't go away when you touch it to the table, so it's possible that you're getting a similar amplification either way, it's just that the rounded fork needs a bigger boost in order to catch up with and overpower the fundamental. Of course, that's a bit of a punt because it doesn't explain why the harmonic is weaker, but still, it's a thought.

I normally watch your videos to the end, though don’t know why. I was an English major in college, and for much of my life I generally avoided math (or as you call it across the pond maths). I generally find your videos entertaining, and I did learn a thing or two every now and then. When you tell me I should work something out though, I usually don’t do that. I don’t have enough interest in such things to do the work myself. I just appreciate watching folks like you do the math so I don’t have to.

Unexpected data is the best data. It is an opportunity to learn something.

the mirror was awesome!! :D

I think this is actually an additional resonance from tension and compression when bending occurs at the root (the place where the prongs meet). Normally I think any bending resonance will cancel itself out as the tension and compression waves will spread out through the cross-sections, negating most when the tension and compression are at the exact same height (the difference in height depends on the precise shape). If bending occurs at the neck, however, the compression and tension waves are vertically displaced, so they don't cancel as they travel through the stem. Notice now that at each half-cycle of the forking-resonance (the mostly horizontal resonance of the prongs), the bending changes sign: inward forking makes compression at the root, and tension at the neck (the part between the root and the stem). The next half-cycle, there's tension at the root, and compression at the neck. Because the signs are changing, the bending resonance is NOT half the wavelength of the forking resonance. Because a negative times a negative is a positive, the bending resonance will be at double of half the wavelength of the forking resonance: there will be a substantial vertical resonance at the same frequency as the forking if the bending occurs at the root. This is more clear if you consider deforming a tuning "T," a tuning fork whose prongs are horizontal. In the middle, tension and compression will produce a particular mode of vibration at the frequency of the "T's" prongs. This remains the case when the prongs are bent upwards at particular angles. As the prongs go to vertical, the vertical component of their forking vibration is minimized, but, unless the shape has been deformed such that resonance no longer causes bending at the root of the fork, there will be a vertical mode of vibration from the resonance caused by the bending of the fork at the frequency of the forking.

If you are curious, you should look into overtones. Over the mic, it was far easier to hear higher, different pitches than what the tuning forks are marked for, but all these frequencies do exist in the tone, regardless of the medium. That is why on the app, you can see several peaks throughout the distribution. We hear the dominant ones.

My thoughts on the round profile fork not having as pronounced vertical frequency as the square profile is; With the the square profile, the side experiencing the compression is being forced to bulge outwards mostly towards the normal of the flat surface as there is less structural strength in that plane, ie, mostly directed up and down perpendicularly to the motion of the fork tines. The forks with the round profile due to their surface shape have some of their mass bulging outwards along the normals of their surface, with less mass being displaced orthogonally to the plane of the fork tines' motion.

I love the manual cutting to a shot of Prof. Hunt's face by use of a mirror.

I clicked the like button an even amount of times... Nothing changed in the end but it's the mashing that counts

The base of your Tuning Fork "Round- vs Square-base" does different Resonance while touching the Table. The peak at the Second Frequencies on the square base caused by the Shape of the base. You see similar effects watching Resonance experiments with Different Material/Particles and different Resonance plates (Round vs Square). It's all about Creating an interference pattern in a mechanical resonance with a different Material shape. The force and the response of the Square structure form are in phase with one another, creating different resonance patterns by the form, and the energy in the vibration increases.

Parker tuning forks?

There are two causes for the vertical vibration in the stem of the fork: (1) The bending force in the juncture of the legs, having the same frequency as the legs (2) The shift of the center of gravity of the whole device, this has the double frequency (the bending of the legs shifts the center of gravity towards the stem, which must respond by moving a little inwards) Which of them is more prominent depends on many factors of geometry and stiffness.

"the same note but one octave higher" sounds right to me. Usually, we talk about C, D, E etc., which is basically the place in the scale (or building block) of a musical piece. If you want to be more precise, you can say "this is C2 and one octave higher is C3". Grand pianos range from A0 to C8 (many of them at least). If you refer to written music, you can call both C2 and C3 just "C", but they are always different notes (in the score). Even two Cs of the same pitch aren't the same, since they appear in a different context... In other words: Don't worry, music is not an exact science :D Or, if you insist on being precise, talk about the pitch. By the way, my fork doesn't do the second octave. But there is a significant difference to most of the forks you used in the other video: The ratio between stem and U-shape is quite exactly 2:1, while the ones you were using mostly look like a 4:1 ratio. I do have noticed, that this video is more than 3 years old, but what is 3 years compared to the history of maths!!!

"It's literally people like you who keep the lights on around here"- From in front of a black backdrop. (I know, I know, there are still lights, but it struck my funny bone.)

The square fork has a much more rigid base (machined out of one piece of metal?), whereas the round one is a bend piece with a welded foot/handle. I find it easy to understand, how higher frequencies are easier absorbed by the less rigid base construction of the round material fork. Thanks for making us think!

In this update we can see more clearly that there actually is a bit of a confusion between two distinct concepts: 1. The note that is sounded/heard (based on the fundamental tone and the harmonic structure above it) 2. The most prominent tone that is sounded/heard (for instance at 1:47 the 2nd harmonic of the A 440Hz) At 1:47 we still clearly hear an A (440Hz), just with a different timbre. It seems the app's output may lend itself to be misread as the note sounded (1), instead of simply the most prominent frequency (2) which may correspond to an overtone different to the note.

One thing that would majorly effect it is how far out the tines swing when they are vibrating. The farther out they bend, the greater their vertical oscillation and therefore the greater the presence of the octave frequency. You can even see visually in the vide the major difference in how far the tines swing between the two forks. Not to mention how the square shape will promote entirely side-to-side motion, whereas the circular shape allows for elliptical oscillation. The geometry of those two motions should make it clear that with the same energy, the circular tines will have less vertical oscillation. The mass of the tuning fork will also have an effect on how prominent the octave frequency is. If the fork is lighter, then it will not have the mass to transmit that doubled frequency into the table which is the amplifier. I could be wrong, but the circular tuning forks appear to be much lighter than the others.

On the ambiguity of the word "note." You might like the nomenclature used in musical set theory. A specific frequency corresponds to "pitch" (ex. middle C, enharmonic notes like C# & Db are the same pitch); equivalence classes of pitches under octave equivalence are "pitch classes" (ex. C); scales and chords can be considered as "pitch class sets" (though scales/chords are usually considered as having a special member as their tonic/root, and pitch class sets don't, though one could certainly construct a "rooted pitch class set"). And there's several flavors of "interval" depending on whether they're ordered/unordered (does ascending/descending matter?) and whether they're between pitches or pitch classes. (Then you get to interval vectors and z-relation...)

As a Material Scientist I can confirm that the surface structure and shape will change how the tensile and compressive forces work and how they dissipate; my best guess is that the compressive forces in the circular cross section are dissipating the forces faster than the square forks, this is part of the reason why it's very hard to rip an unblemished circle in half just by pulling on opposite sides rather than with a similar square. This may be part of the reason that the circular forks don't hold the secondary tone for as long as the square forks do.

So, the tuning forks have two main frequency, the base frequency and twice it, as shown by the two peaks in the spectrum analyzer software. When on the table, both still shows, but the up/down double frequency) can dominate because amplified by the table, whereas the fundamental frequency is not, it is just transmitted by the air. Maybe the round shape is better at producing the fundamental frequency, and even the amplification by the table is not enough to make the double frequency mode dominant. So, suggestion follow ups: 1) do it in a vacuum, where the only sound will be if the microphone is touching the table 2) do it far from the phone, the sound will travel well and far in the table, but the sound in the air will not propagate as far 2') same as 2, but put sheets of solid material between the tuning fork and phone to block direct sound waves in the air, further reducing that component. Now, I wish I had a bunch of tuning forks, but I am ok learning what others do without doing it myself in this case.

1:30 So many peaks at higher multiples of the base frequency.

There's another way of interpreting this phenomenon. A kinetic wave travels between each fork prong. And on the half-cycle, the table is compressed by the fork and the fork rebounds almost instantly because of the table's bulk inertia. This causes a vibration of twice the tuning fork's natural resonant frequency to be produced.

Since you're acknowledging the pedantry, it's probably worth noting that, even within the definition you intended, a musician would still say that it's the same note... and be correct. The thing is, if you have a series of harmonics, the human ear tends to perceive the lowest pitch in that harmonic series as being the pitch of the note (this effect is so strong that, in some cases, you can use a series of harmonics to convince the human ear that it's hearing a lower note that isn't actually there because the overtones present usually come about as harmonics of a lower fundamental); this is called the fundamental frequency for a reason. I didn't pay as much attention to the spectra in the last video but, in this video, it's very obvious that the natural frequency of the tuning fork is present in the harmonic series in each case, and thus the "rated" frequency of the tuning forks is the fundamental frequency of the sound being heard either way. What's changing isn't, strictly speaking, the pitch of the note, what's changing is the timbre, the relative distribution of energy between the different harmonics. When the fork is held normally, the fundamental frequency is also the frequency with the highest proportion of energy; it's closer to a pure tone at that frequency. When the fork is placed on the table, the first harmonic content increases dramatically relative to the other harmonics; the fundamental frequency is still there, but a lot more of the energy is now in the first harmonic (interestingly, this means that it comes closer to the energy distribution of the human voice, which puts most of its energy in the first and second harmonics). So, the quality of the sound will be different - it's less like a pure tone generator (or a whistle), and now a more layered sound. Still the same pitch though. The interesting physics remains, of course - why does the timbre change when placed on the table, and what influence does fork shape have on this? That said, you took the time to address the pedants, so just thought I'd point this distinction out.

fourier transform of harmonics explains this. the squared tuning forks are creating a waveform with higher harmonics, Either a "saw" wave, which contains every whole harmonic, or a "square" wave, which has every other whole harmonic, then when you press the base of the tuning fork to the table, you are muffling the fundamental frequency, and the energy lost is partially added to the higher harmonics as constructive interference. this difference in wave shape is caused by the forks being angular, IE having vertices between each prong. The curved/circular symetry, are oscillating closer to a pure "sine" wave with far fewer harmonics, and more of the energy lost on contact with the table, is lost into the table very quickly, and any higher harmonics are the harmonics of the rest of the body of the fork, rather than the harmonics of the prongs. This is based on my experience making electronic music, and using additive and subtractive synthesis.

I would think the reason the effect is less pronounced for round tuning forks is that the oscillation is radial (around the normal position of the tine) rather than linear (across the normal position of the tine), thus the tine doesn't actually have much of a vertical oscillation component. I'd point a slow motion camera close to either when they're oscillating and look at how they move.

Ask the slo mo guys to slo mo a tuning fork!

Looking at a spectral analysis only gives you part of the story. What you need is an oscilloscope and some piezoelectric transducers. A microphone simply doesn't seem to be cutting it. Another way you can pick up the motion of a ferromagnetic object without touching it is using a coil of wire with an iron core that has a magnet stuck to one end. The coils found inside relays work excellently and can be very compact.

Matt did you know that trumpets can make different notes?

@4:24, almost every physicist everywhere screamed at the screen when he said "centrifugal force"

I am a musician and I use "note" for exact frequency too. It's C note, it's C note too, but not the same. And I use "note" for # because they are notes too, it's just us who decided that C Major harmonica is superior.

In some musical contexts, the term “pitch class” is used to describe, for example A-440 (A4), A-880 (A5), A-1760 (A6) and so on as one group of related frequencies, differentiating each individual frequency (think of it like modular arithmetic)

This is pretty awesome. KZfaq as peer review. I love that so many people took their own time to verify this themselves and provide feedback. It's a beautiful thing, the scientific method.

Awesome, I'm off to Hathor temple Egypt in the next couple of weeks, I was trying to look up the best tuning fork to take and found you 😊

When you 'square wave' an otherwise sine wave frequency, you naturally create a rich set of harmonics (a doubling) of the primary frequency up the line. I thought of that with those tuning forks. One had rounded edges and the other one had squared edges. A funny yet apt analogy :)

I think that the square cross section vibrates as shown on the previous video. However a circular cross section can vibrate in a different mode. The circular cross section could sort of rotate rather than just going back and forth. which would significantly reduce the effect of the centripetal force. You could confirm or refute this by taking high speed video of the end of the fork as it vibrates.

I just tested this with a S&P forecep (precision tweezer) from my dissection kit. I've noticed before that it vibrates similarly to tuning forks. Saw this video, downloaded a spectrum analyzer app, and tested it. Two peak frequencies 129 and 258 Hz. In open air, 129 Hz was the higher peak and on the table, 258 Hz was the higher peak.

This really should be called Tuning Fork 2: The Retuning

gracefully gracious as ever, sir

I'm pretty sure that, when people were talking about harmonics, they were talking about the harmonic overtone series. That is not even remotely the same thing as "trumpets can make different notes". The harmonic overtone series means that for any (analog) instrument, even while nominally playing a single note, many additional higher frequencies are heard and contribute to the full sound of that note. The first harmonic of the overtone series is an octave higher than the base note (2x the frequency), which is probably why people were mentioning it in the previous video. The second harmonic is 3x the frequency, which gives an octave plus a fifth. The third harmonic is 4x the frequency (2 octaves, obviously), the fourth is 5x the frequency (2 octaves plus a third), etc. All these frequencies accompany the base note when an instrument is played, because if the chamber/string can resonate at the base frequency, it can also resonate at any integer multiple of the base frequency. This is also why we see spikes at regular intervals on the frequency graphs in the app.

The point about it being the same note is not that your nomenclature is wrong, but rather for the purpose of what the tuning fork is designed for it does not matter if it vibrates at 440 or 880 they are both an A and will allow me to tune my instrument. So it is a different pitch but not a significantly different note for the purposes of tuning. Some instruments can not play A440 it is still used as a reference. I think this is the point people were trying to make.

I think that the round tuning fork arms oscillate in a circular pattern rather than on the same plane. If we attached pencils to the ends, the rectangular tuning forks would draw straight lines on a piece of paper and the round tuning forks would draw ellipses.

No idea about the mathematics of this, but I play an instrument and these are called overtones, on a saxophone you can use manipulate the instrument to play much higher notes than the instrument would normally play without having to change which keys are being pressed

I thought you were going to mention something about hearing overtones of the fifth of the scale at 4:25 of the original video. An octave is double the harmonics. So if A=440 and A=880, the fifth E is roughly 660Hz (intonation rules aside for a moment.) When he held the tuning fork to your microphone I heard those harmonics. You would probably like the maths of the different rules of tuning - Just intonation vs equal tempered and so on.

Thanks for showing us what a square and circle look like.

You play one and only one quaver on the like button. This was interesting...as a percussionist, I rely on a tuning fork to know how to tune timpani. I was worried at the beginning thinking there was unreliability in their pitch, but finding out the pitches were an octave...and the same...note...haha, I am much more assured. Is a possible explanation the fact that the arms of the fork directly move the air near the end. That sound is very hard to nail in and hear. It's gone within 2 inches, and I have never relied on that method for hearing a tuning fork while an ensemble is playing. It's too easy to dampen the fork in your hair, and too hard to find that sweet spot where you can hear it at all. So instead, I place the end of the tuning fork directly on my Tragus, and even sometimes plug my ear with it. It is way more consistent, and my ear then becomes the "table" and I can lock in on that A-440 no matter how loud it is around me. But that is a very different mechanism, being conduction, vs the incredibly inefficient "speaker diaphragms" that the arms of the fork make. I wonder how that in itself plays in this? I do know that in order for speakers to amplify properly, they need to separate the two sides of the vibration, otherwise the air just would swirl around the cone, and that explains why a tuning fork is barely audible until your ear is placed within the vortex of air vibrations.

These two videos were very interesting. Thanks!

My thought on the doubling is that it depends on if the fork is bent at all slightly out of parallel; If they are parallel, (high quality fork) then each half wave (tines moving inward or outward) causes the bottom of the fork to thrust outward axially, causing the doubling. Each half wave causes a half wave in the air but 2 waves in the jackhammer end of the fork. If the tines are not parallel I would imagine the half wave (again, only tines moving inward OR outward) dont both cause an axial thrust, and thus the frequency matches. This jackhammer axial force is not from the bending of the material, rather the center of mass moving as the tiny amount of oscillation causes base to vibrate. Gonna need a microscope and a very very high speed camera.

The resonant frequency of the fork in your hand corresponds to the arms flapping uniformly and the stem translating/moving up and down. The higher natural frequency corresponds to the stem being stationary, and the arms "clanging".. holding the stem against the table forces the tuning fork to vibrate in the "clanging" mode only, because the stem cannot translate anymore. Source: 5 minute FEA frequency analysis ;)

I love that you can see all of the harmonics appear at once...

Not sure if it's been commented before but the square fork seems to be made from one piece of steel the round one seems to have the handle attached, a different construction method possibly welded on in some way. Great video's and I'm an end watcher :D

Every element has its on frequency in which it likes to ring. And the thickness of the tuning fork and all other qualities come to play, determining how much it likes to vibrate in different fequencies when its pressed against the table, which is ofcourse, made of completely different elemrnts.

I think it's the similarities in the geometries, small and large, of the two structures that determines the resonance and the amplitude of the sound. I think this effect is extremely valuable in the understanding of how energy and information is exchanged in the Universe. I'm pretty sure that it is the particular vibrations of the waves that travel through the blood, plasma and spinal fluid of our bodies that rings the bells of the geometric structures, enzymes in the mitochondria and ganglion around the Pineal, that facilitates the attraction of the electrons from the fluids onto the structures and the energy and information that is contained in the waves of the electrons and the protons are moved similarly to produce a pressure gradient and the flow of current in the smaller oceans of the cells. I think this is basically how energy moves at all levels, it's the structure that attracts the waves that it's tuned to. Just like a negative thought attracts other negative thoughts, angry folks find folks to be angry at. When we feel that we are in Love, negativity tends to have little effect. It's the emotions that we choose to focus on that determines the predominant vibration of the waves cavitating from the Heart and it's these waves that transform the structures that they travel through because all structures are in fact standing waves of entangled electrons. I'm just trying to say that Love is the power of the Universe. Peace and Love for everyone. 💞🎶🔯⚛

When the tines of the tuning fork bend the position of their centers of mass change with respect to the bottom of the bottom, thus the bottom will oscillate at twice the frequency of the tines so this mechanism may also contribute to the sound when the fork is on the table. This effect will depend on the mass of the tines, i.e. on their cross section and may thus explain why some tuning forks exhibit a larger effect that others.

Maybe a slow-motion close-up of the tips of the forks would be interesting. I wouldn't be surprised if the square forks vibrate in the plane of the fork, while the circular ones dont.

my terminology here will probably not be the best but i believe that this requires a check: what if the oscillation of these tuning forks differs (I am guessing that the forks have more of a circular movement, thus stretching between two axes and in turn the vertical oscillation being minor.) the square shape on the other tuning forks should prevent that from the shape (extra mass on each corner etc) edit: should also check if contact with the table affects the oscillation (making it completely circular from say elliptical)

I like the horn on your wall there, Hugh... And the mirror.

I appreciate the attention to accuracy with the use of the word 'note'. I'd like to add that at least with stringed instruments (not sure about others), harmonics are a specific way of playing certain notes. Rather than pressing the string against the fingerboard (effectively shortening the length which vibrates) you just lightly touch the string so that the whole length vibrates but not at its fundamental frequency.

I suspect that there are two effects going on, the one originally described and the one described today. And, which effect dominates largely has to do with the mass of the tuning fork's handle versus the tines' mass. In the ones which don't work, the inertial mass of the handle is large enough relative to the mass of the tines to dampen the higher order oscillations. You can tell that I'm right when you look at the FFT graph. You can see that for the normal forks, the first harmonic is about twice the amplitude of the fundamental. On the abnormal forks, the fundamental and first harmonic are about equal. This totally makes sense if, in all forks, there are both mechanisms at work, but in the abnormal forks, the inertia related oscillation is being dampened a bit.

There's a lot of variables at play there. Shape, type of metal, forged vs. welded handles, and probably several more I'm not getting off the top of my head. Sounds a deeper investigation and control of the factors is needed. Also, high speed cameras may very well shed some light on this mystery.

I’m literally doing this experiment tomorrow for science class, thanks for the answers XD!!!!

Good update. I would have said something too had I seen the first before this one came out, because I've played around with tuning forks and tables quite a bit and they've been the same pitch (which I think is the word you want rather than note). They've also been the small round silver kind, so that matches this video's results.

The rectangular tuning forks will be more likely to have modes existing in only the stimulation direction, and are less likely to transition to the perpendicular direction. Unlike those, the round ones are able to vibrate in any direction perpendicular to the tine's resting direction. This means it could vibrate with circular rotation and not have any momentum change in the, in this case, up and down direction.

I've been a musician my whole life and never come across a square tuning fork like these. All mine have been round. Very interesting!

Interesting note on a similar effect~if you're familiar with the pan flute, adding a cap onto the lower end of a pipe will lower the frequency by an octave (it might have been the other way around :P). The explanation I heard was that this doubles the path length that sound waves must travel before leaving the tube, changing the phase accordingly. It sounds to me like the tuning fork situation may involve a similar effect. However, I struggle to see this as an analogous situation, so probably not. Still pretty neat tho

The reason for the doubling of frequency was that the rods reached their maximum height when they were between the right and left extremes, and therefore two times per oscillation. My theory is that on some tuning forks the maximum height of the rods is not reached between the two extremes, but on one of them. Then the maximum height will only be reached once per oscillation, and that is why the frequency is not doubled.

Keep making more than one noise Mr. Parker, and I'll keep watching!

I think that the big difference between the two different bases is that the square one oscillates around the center, giving us the doubling that we saw in the previous video. But for the rounder one, the motion does not stay in the middle, but iris more pronounced when the fork is bent outwards. this would cause a difference based on geometry.

Tuning Fork Mystery: Possible Explanation This link is to a diagram I drew to help explain. www.dropbox.com/s/t8ua2xtx4vr6zo4/TuningForkDiagrams.jpg?dl=0 Apologies for any particulars in the diagram that are not exact. This is all a thought experiment, and I don't know all the symbols & equations. When striking a tuning fork each will vibrate at a set frequency (Figure A). For this example, 440 Hz. This frequency is heard by our ear as the sound wave propagates though the air (Figure B). 440 is the fundamental frequency, however, natural doublings occur known as the harmonic series, but are too faint to be heard without amplification. When placing the fork upon the table, each prong oscillating at 440 Hz combine together at the base of the fork (Figure C). The individual frequencies add together to equal 880. Something to note is while the prongs are out of phase, the inner "U" is smaller than the outer "U". This difference likely contributes to why they don't cancel out completely, as the time it takes the outer edge wave to travel the inner edge wave has already passed. This allows the wave to continuously "feed" the "output" frequency. This may be akin to how a cardioid microphone works. Another note is that the out of phase prongs do cause the wave to cancel a distance from the fork. The next part is related with the difference in tuning fork styles, square vs round. The square fork has surfaces exactly 90 degrees from the direction of the prong's travel (Figure D). Thus when the wave attempts to propagate through the material, the phase difference of the sides prevent it from traveling around the outside. Thus forcing it to only travel down the inner and outer sides. Because of this they waves don't cancel themselves out on the cross section as they are prevented from traveling around the square. The round fork, however, does not have the sides 90 out of phase with the inner or outer edge. Thus when then sound travels around the circumference of the cross-section some of the waves cancel (Figure E). Meaning that the doubling frequency is noticable for a short duration, it quickly cancels out as compared to the square fork.

Keep up the great work. I'm very interested to find out exactly why shape have such an affect. Love the use of the mirror as well.

I think it's more likely that a square profile will bias toward a back and forth vibration, as explained in the first video, whereas a circular profile won't experience such a bias and is likely to vibrate in a circular or helical movement which will not result in the same phenomenon.

A circular cross section would more easily transfer energy to a transverse vibration (left right vs forward back; I'm considering the doubled harmonic to be up down) by moving in a circular/elliptical path. This also removes much of the up and down momentum as your change in height is less across the swing of the fork for a circular path vs a linear path.

My vote is that the answer to the frequency observation showing up on some tuning forks and not others could be shown in a slow-mo video, or with the use of a strobe light at the frequency you hear. I think there is more to this story.

There is a directionality to the tones in relationship to the shape of the fork. The sound coming from the space between the forks perpendicularly, and the sound coming from the sides of the tines themselves........

Unless my eyes deceive me, I’ve got the exact set first demonstrated here. John Walker - England. I’ve always noticed this phenomenon whilst tuning pianos, although I have noticed the medium plays a large role. If I hold the vibrating fork to the piano’s wooden frame, the effect is slight, and quickly fades. So I always hold it to the plate (the cast iron frame) where the effect is stark and long-lasting. I think metal upon metal maximizes it, whereas other mediums tend to dampen it. -Phill, Las Vegas

Looking at the footage that you captured, with the square tuning fork, each harmonic is almost equal in volume. However the circular 'fork seemes to have more of an eponential decay as the harmonics increase the volume of each harmonic decreased by factor "x". Interesting to see if this is true for all curcular tuning forks or just the one used in this video... Keep up the great mathematical work, can't wait for the next one! :D

Please forgive me if I sound silly, but wouldn't the circular/tube-shaped fork be prone to vibrating in a conical way (viewed from the top it would appear clockwise or counter clockwise), where the square forks will be thicker on either the x or y axis. So by placing the fork on the table you stabilize the one axis' movement more than the other, allowing the fork's non dominant tone to peak? Also, please try this test after striking the fork as usual and then holding it at 90 degrees to how one usually does when placing on the table (to see if the hand gripping it is stabilising the one axis of movement). And, as though that weren't enough to ask of you, please try by striking the fork perpendicular to how it's intended to see if a similar phenomenon will occur. EDIT: I could've mentioned a similarity to a harmonograph having it's x and y pendulums being adjusted, so please imagine that I did ;) EDIT 2: I literally paused to comment before you mentioned harmonics and holding the fork.... I'm pretty embarrassed right now. Still think the circular forks are rotating more than the square forks. Please consider my request. lol Thanks in advance.

I love how you title the first video ‘The Tuning Fork Mystery’, but it's only later that you realize you've come across an actual mystery.

The square forks are milled by a machine. so no inner structural damage to the atoms. The Round ones are bend to the shape of a fork. So the material has become a different structure (same as heating and cooling down Iron to make it harder)

The phenomenon is easy to understand if you think about how the tuning fork's center of mass moves in relation to the base of the tuning fork while its two prongs are vibrating. When the prongs are displaced from their neutral position, a tuning fork's center of mass is displaced -- ever so slightly -- 'down', toward the base of the tuning fork. This displacement occurs twice each complete oscillation of the prongs. It is this 'up and down' movement of the center of mass -- at twice the frequency of the prongs -- that is transmitted to the table top resulting in the octave boost. All tuning forks do this, regardless of their cosmetic differences.

That round tuning fork looks like it was welded together from two different pieces (fork and handle) and the square one was cut as a solid piece. This might also be a contributing factor.

Given the difference in shape, could it also be the involvement of the surfaces? A square surface is going to be struck directly across the entire inner surface of the tines by the wave emitted by its counterpart, whereas the round surface is only going to be struck directly by the wave across a very narrow line. I would think that this would also be a major consideration. Alternatively (or additionally) the shape will also affect the internal propagation of those waves. Just a thought.

Not only does it show a spike at double the frequency, but more at each further doubling. And they're alternating between slightly higher and slightly lower frequencies. The harmonics are more than obvious.

it’s just simple harmonics. On the spectral analyzer, you can see MANY obvious spikes beyond the spike at 880 Hz. Although the octave may be the most pronounced, it’s just harmonic series. If you want to see some harmonic stuff, check out the Undertone series. (i’m sure i’m completely missing the point here but whatever)

In modern music, the note A0 is 440 Hz, the note A1 is the 1st harmonic at 880 Hz. With the number associated, it appears that they are different notes :-)

A guitar string vibrates at several different frequencies at the same time - they are not all the same note. It vibrates at a frequency with the whole string shaking back and forth as one piece - that's the fundamental frequency. It also vibrates in halves, quarters, etc. - double the frequency each time, but the same note. BUT - it also vibrates in thirds, and fifths, etc. - those are different notes. Basically strings play chords when they vibrate, and when you reinforce those same frequencies by playing several strings, it sounds good. The human ear likes those frequencies that come together on one string. At least the ones that come strongly, which are basically the ones with small denominators of "shaking fraction."

All tuning forks have a torsional component as well. Its just more pronounced in the square legged case. Put a tuning fork in front of a precision strobe, and you'll visually observe the effect.

circular tuning forks would oscillate in ellipses as opposed to the square tuning forks which would vibrate in a more straight, back and forth pattern, this could also change the frequency of the bottom of the tuning fork whether or not it had a flat bottom and also might attribute to the faster diminishing of the higher frequency because i think, i havent done the math but having a elliptical oscillation uses more energy so the frequency would diminish faster

I suspect it's something about a "hard" interface vs a "soft" interface for reflection at the base that emphasizes the harmonic more than the fundamental. Even on a violin you can get a harmonic out if played appropriately. The finger on a guitar string is not a good illustration of selecting harmonics. That's selecting primary resonance lengths and tensions, which define the base of a mostly harmonic series. Harmonics are modes that are at multiples of the fundamental. A pure sinusoidal resonance is free of higher harmonics. Anything periodic that deviates from a sinusoid (like a square wave, triangle wave, or impulse train) will have a more complex timbre, and will exhibit harmonics. Nonlinearities in amplifiers can add harmonics to even a pure sinusoid.

Hello, i know no one is going to see this, but the reason this is ocurring is that when you listen to the signal produced by the fork in the air it is just the constructive interference of both sides of the fork that is transmitted, hence the normal First Harmonic higher than the others(normal/intended situation). BUT, when you use the bottom part of it to listen, what happens is that since the energy of both the sides of the fork is concentrated in the midle part, the signal it produces is a modulation of the original signal, but with energy concentrated in the 2nd Harmonic since the lower part is minor in length(About half of the other side). So essencialy two effects here: -concentration of energy in the bottom part -geometry leading to modulation into 2nd harmonic At least is what my Telecommunication engineering knowledge points to! Feel free to ask any questions guys.

I always knew I was awesome. Thanks for confirming it

All the harmonics are already present in the waveform, touching the end of the tuning fork just reinforces one or damps out another. This phenomenon is also present in pretty much all musical instruments, most obviously in stringed instruments. So the explanation has to be something that is not specific to the shape of the tuning fork, as that shape is not duplicated in those other instruments.

Hi, I enjoy looking your video. Always refreshing. Concerning this video, in my work with my colleagues we study piezoelectric resonators and noticed that the shape (square, shaved corners or round) influence very strongly the resonance and harmonics measured. We get purest signal with harmonics strongly reduced with round shape.