The Tuning Fork Mystery: an unexpected update
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- Опубліковано 26 бер 2018
- Here is the original tuning fork mystery video.
• The Tuning Fork Myster...
But some people could not get the frequency doubling to work. Now we think we have the start of an explanation.
More updates to follow as Hugh and I investigate it further!
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Using the mirror for the close up is just delightful.
its one of those things that a lot of people wouldn't think of
An elegant solution when the reverse camera isn't worth the trouble.
Realized its a mirror, mind blown
teddy boragina It's*
The fact that you didn't even notice it conveys how well it worked
That's a really smart use of the mirror
I scrolled down, read the comment, wondered what mirrior, scrolled up and _suddenly; 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:)
I forgot to mention my suggestion: try using a tuning fork and a resonance chamber; then you'll probably be able to hear the overtone much more distinctively. If you don't have a proper box, the body of a guitar or a cello should theoretically work.
This is a great contribution thank you
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.
Thanks for showing the shapes at 0:48
I couldn't remember what squares and circles look like without it
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.
etorigoe This was exactly my thoughts.
That was my initial thought as well. I wonder if a tuning fork with a triangular cross section would produce the same, or more of an, effect than the square cross section.
I would like to make a FEM-analysis however I don't have a preprocessor...
This was my first thought. If this is analogous to rubber strings, then my experience from childhood says the one with the circular cross section goes around in an elliptical path. Hence the frequency doubling effect is there but weaker.
Upvoting this idea as well. Probably time for a high-speed camera!!
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.
My guess is that there are multiple physical effects that cause the fork to vibrate at specific frequencies and the geometry and material of the fork might influence the strength of these effects, which might create the different strength of each harmonic
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.
i would kill to see one of those internal stress images in super slow motion for a tuning fork
Make it out of glass and use a polarizer. That's it :)
Better yet, make it of plastic.
Install Ansys.
The joy I would get out of someone making a tuning fork out of glass without really thinking about it, and immediately smashing it against something to test it is astounding.
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.
YAFU2 I wouldn't think so beacause remeber the sound is caused by the movement of air, not the force onto the table.
Aaron Quitta But it is not the air between the tuning fork and the table which generate the sound. The tuning fork makes the table vibrating at the same frequency and the table + the tuning fork makes the air around vibrate.
Dark Thats a fair point. I don't know then.
I have a square cross section tuning fork here with the same type of base as the circular one in the video, and the effect is as pronounced as the square ones used in the video.
Just some late evidence.
It's not about the surface area on the table, I'm pretty sure when Hugh said "geometry around the base" he meant the base of the forks where they intersect the handle, not the base of the handle... Had to watch it again to clear that up in my own mind too. It's the mechanics of the geometry at the intersection of the forks with the handle.
The weaker that intersection, the less likely you'll get the octave change between the forks and the handle.
-Stronger intersection: centrifugal (vertical when the fork is upright) force of the forks dominates. Hence double the frequency of the forks From first video.
-Weaker intersection: Compression/tension dominates in resonance with the forks.
Melted my brain for a while too ;p
Unexpected data is the best data. It is an opportunity to learn something.
There is no agreed upon answer.
en.wikipedia.org/wiki/Data_(word)
Well said!
Except when it's a shart.
I love the manual cutting to a shot of Prof. Hunt's face by use of a mirror.
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!
I clicked the like button an even amount of times... Nothing changed in the end but it's the mashing that counts
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.
the mirror was awesome!! :D
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.
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 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.
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.
This is pretty awesome. UA-cam 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.
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.
"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!!!
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...)
These two videos were very interesting. Thanks!
"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.)
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.
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.
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.
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.
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 😊
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.
gracefully gracious as ever, sir
This really should be called Tuning Fork 2: The Retuning
Ask the slo mo guys to slo mo a tuning fork!
they already did! ua-cam.com/video/VCERs0v1OoI/v-deo.html
Rather a variety of tuning forks, no?
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)
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.
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
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.
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 :)
Great stuff, love your videos....
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.
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. 💞🎶🔯⚛
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.
Keep making more than one noise Mr. Parker, and I'll keep watching!
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.
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.
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.
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
1:30 So many peaks at higher multiples of the base frequency.
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.
I’m literally doing this experiment tomorrow for science class, thanks for the answers XD!!!!
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 am thoroughly impressed that you guys followed up! ;)
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.
Parker tuning forks?
I mean, it still works, but it decays faster than with some tuning fork geometries. So you gotta whack and place on the table quickly, I suppose.
Also, maybe one could devise a geometry of tuning forks that doesn't make that happen. That would be pretty neat.
If ya can't drive 'em, how ya gonna park 'em?
Fred
I think that tuning as a whole is a typical Parker thing. No matter what tuning system we use, it's always close, but not quite right.
Time to go tune a piano REALLY QUICK.
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 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 ;)
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
Thank YOU, Matt!
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
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.
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.
I love that you can see all of the harmonics appear at once...
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!
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
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)
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.
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 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.
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.
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.
Something interesting that may or may not have a similar foundation to your tabled tuning forks, but might be worth researching.
On pipe organs, the length of the pipe determines the pitch. Easy. If you close that pipe, it will make the same pitch it would've made if you doubled its length.
At least, that is what I recall from a class 20 some years ago.
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.
It would be interesting to see if the difference in the cross sectional shape of the fork tines promotes different oscillating modes. This could be observed with a strobe light. I suspect that round tines are able to move in an orbital pattern, and hence produce a much lower y component of oscillation. I suspect the square cross section would have much more variation in spring coefficient with respect to angle about the axis of the tine and is hence locked into the simple planar mode of oscillation as described in this and the previous video. That could explain why round tined tuning forks have a 2nd harmonic which decays much more rapidly when pressed onto a hard surface, as the oscillating mode transitions from simple planar to orbital.
noted! and brilliant comeback !
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 like the horn on your wall there, Hugh... And the mirror.
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.
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.
The short horizontal parts of the beams also bend. When the stiffness of these parts is low, then there is more bending for the first Eigen mode. This bending will lead to displacements of the stem attachment location relative to the vertical location of the overall center of gravity. So this will lead to movement of the stem with the Eigen frequency. I am quite sure that this effect is much larger than the lateral contraction of the material in that Region, because the translations due to bending over a few millimeters are much larger, than the associated normal strains, and the normal strains are much larger than the lateral strains.
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.
@4:24, almost every physicist everywhere screamed at the screen when he said "centrifugal force"
Thank you, Matt! Subscribed, belled up and all that stuff, of course.
Great vid, thank you
Using harmonics for instruments is different than just playing different notes!! It's producing the notes with a specific technique! You can press a guitar string in the exact same location on the string two different ways to make a different frequency. I highly recommend you ask a guitar player to play some for you, because it's actually really cool :D
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.
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.
But you don’t “hear” the E at 660, you hear the E an octave higher at 1320, right? The harmonics are integer multiples of the fundamental frequency.
Bingo!
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 believe by lightly touching, say, in the middle, you are forcing a node at the point, eliminating original fundamental and all odd harmonics (or is it even? I forgot) producing a new note.....?
I keep confusing myself.
Exactly. It's possible to do it for several different harmonics on the same string, but it gets more difficult for higher numbered harmonics.
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)
0NBalfa0 that was my thought as well.
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........
I was wondering if table composition plays a part? It would be interesting to see if you place the fork onto different surfaces if it would change how the dominant frequencies react.
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.
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.
I thought that the bending of the forks would move the center of mass of that fork. The sideways movements cancel each other out, but it also moves slightly in the vertical (curved fork has a slightly lower center of mass). The square forks might move more in straight lines, where as the rounded ones could have more of a circular motion to them.
I'd be interested in seeing a slow motion close up, comparing the two.
I imagine the rounded fork ends are swinging in a circle when viewed from above and vs more straight back and forth in the square forks. Between the circular motion and the smaller fork to table interface the doubled frequency isn't able to conduct much more than the primary frequency.
My instinct is that the difference may have more to do with mass vs. stiffness of the tines than shape of the base. The "doubled" vibrations at the base will be driven by the vertical displacement of the centre of mass, which varies with the sine of the amplitude of the fundamental vibration. In smaller / stiffer forks, this value will be negligible, allowing the fundamental to dominate, EXCEPT WHEN STRUCK REALLY HARD, as Hugh demonstrated. It decays quickly.
I suspect round cross section tines are stiffer for a given mass than square section ones.
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.
Neither a musician, nor an engineer, however, I notice that the troublesome (round) forks seem to all have a sharper transition from the fork to the handle.
That is to say, the base of the fork is essentially a U-shape with a handle projecting perpendicular to the point of contact. By contrast, the forks that you were using in the last video, as well as the forks that behaved as expected in this video have a radius as the fork transitions to the handle.
Because waves tend to travel much more effectively around curves than sharp corners, I believe that a larger portion of the amplitude of the vertical component of the fork's motion is able to translate down through the handle with the radiused transition.