The Tuning Fork Mystery: unexpected vibrations

Check out the puzzles over on Brilliant!
brilliant.org/standupmaths
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There is a follow-up video to this one looking at some other strange vibrations viewers noticed.
The Tuning Fork Mystery: an unexpected update • The Tuning Fork Myster...
Possibly over-qualified for this video, Hugh Hunt is a Cambridge University Reader in Engineering Dynamics & Vibration.
www.eng.cam.ac.uk/profiles/hemh1
See some of the fun stuff he does without me.
www2.eng.cam.ac.uk/~hemh1/
Check out Mirko’s three-sided coin simulation here.
almondbread.github.io/tscsim/
All the links for the various three-sided coin resources are here.
think-maths.co.uk/threesidedcoin
CORRECTIONS
For the people who couldn’t get it to work at home: • The Tuning Fork Myster...
- Let me know if you spot anything else!
Thanks to my Patreon supporters who made these ridiculous projects possible. Here is a random subset:
Jon Ivy
Erin Cassie
Jade Bilkey
Laura Dale
Samuel Ytterbrink
Support my channel and I can make more videos:
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Music by Howard Carter
Filming and editing by Trunkman Productions
Audio mastering by Peter Doggart
Design by Simon Wright
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
Maths book: makeanddo4D.com/
Nerdy maths toys: mathsgear.co.uk/

[@AgglomeratiProduzioni]

6:09 Best hand-drawn sine ever

[@JoshuaRando]

It is so annoying when people use half circles!

[@DerpMuse]

I found my type of people lol. It was so even in his pace and periodicity I couldn't help but feel satisfied even after continuing when the centre line has stopped. Bravo.

[@eideticex]

Joshua Rando. It must really annoy you that most spheres and circles drawn by computer algorithms are using using sine and cosine curves.

[@gnugo9600]

look at his wrist and the forearm while he's drawing it. very similar to a piano player having done their homework practicing legato slurs... never occured to me this helps improving sine drawing skills as well... btw. has anyone else spotted the grand piano with the pile of scores? ;)

[@transdimensionalist]

609 good numerology :)

[@seanm7445]

This video really resonated with me.

[@Ikkarson]

Btw if you tap the fork then roll it between your fingers, the Doppler effect between both branches will produce two notes, one slightly higher and one slightly lower than the fork « at rest », and the interference between these create yet another note.

[@macronencer]

Antonin Caors - this comment deserves to be upvoted more! That's fantastic. I remember waving tuning forks about when I was a kid, but I don't think I ever tried that. I will now :)

[@kaaiplayspiano7200]

@@macronencer not reddit it called like

[@macronencer]

@@kaaiplayspiano7200 "Up" and "voted" have meanings independent of Reddit. The words existed first :) Had I written "liked", the nuance of the idea of voting for something *to make it rise higher on the page* would have been lost.

[@jasonbailey9139]

This is giving us a pretty good look at how long your production cycle is. Hair for the interview. Bald a few videos ago. Hair growing out in the outro.

[@jetison333]

Jason Bailey I imagine they recorded a ton of these and he's releasing these slowly

[@jiggely_spears]

Like his head releases hair?

[@nadiak4167]

Yet, the same shirt :)

[@dliessmgg]

The thing he showed at the end with the bouncing so that only every second or third vibration hits excited me the most, because it's the first time I've see the subharmonic series represented in reality, and not just as a theoretical construct.

[@Bladavia]

You can also do it by touching a piece of paper with the fork, and you can also do it on a violin by pressing the bow very strongly on the strings.

[@ZipplyZane]

Blad That makes me think maybe the action in vocal fry is actually using a subharmonic, since its made with very pressed vocal chords.

[@Bladavia]

ZipplyZane Actually I think this is also the "beginner violonist sound". I saw this in a video by Adam Neely

[@UndoneFakeJesu]

Is it actually a representation of the undertone series of the fundamental, or a new tone created in a new manner with its own overtone series? The fundamental frequency itself isn't convincing and I don't remember having seen anyone demonstrate with accurate measurements that actually produces an undertone series as opposed to just a new fundamental with a new overtone series with a different Fourier series approximation

[@Bladavia]

kzbin.info/www/bejne/pWXNmIOafNeNj6s

[@BunniBuu]

This phenomenon is used practically in a lot of music for string instruments (guitars, violins, etc)! If you lightly hold a string down, you can double the frequency it vibrates at, causing it to ring an octave higher :) There are all sorts of variations on using this (touch harmonics, pinch harmonics, natural harmonics) and they're all very valuable to musicians :)

[@StarryNightGazing]

BunniBuu the touch harmonic happens because you force the second mode of vibration of the string by creating an artificial node, not sure it has anything to do with this 😬

[@BunniBuu]

Stargazer I'm no expert, but I thought touch harmonics produced two octaves since they first reduced the length of the string (as you mention with the node), but also create a harmonic the same way a natural harmonic would. I don't personally play any string instruments beyond an elementary level, so my knowledge of the physics of them could very well be off!

[@StarryNightGazing]

BunniBuu you do not reduce the length of the string but it's the whole string that vibrates with half the wavelength 🙂

[@GrumpyMidget10]

Never before have I seen such beautiful, hand-drawn sin/cos waves. Well, done Mat, at least you can draw that (cough - parker circle - cough)

[@Erik-yk9zf]

I wonder if his hair grows in and out like a sine wave

[@wynautvideos4263]

Lol

[@pierrestober3423]

I can draw a sum of perfect sin functions

[@jujumw5918]

What an incredible simulation ! Great work Miako

[@ben_jammin242]

The tension on the rope of a swing while swinging made brilliant sense!! thanks! Long time fan of the channel

[@blazep5881]

5:37 that was a Parker wave of a graph

[@sitearm]

I like this one .. learning something never perceived / noticed before .. ty for producing and posting!

[@koenth2359]

This is great stuff. I knew there was an issue with tuning forks and double/half frequencies, but only now I understand what it exactly is! Thank you so much. By the way I have two tuning forks, one labeled 440 Hz and an older one labeled 438 Hz. Fun to hear the beats when they go together!

[@slazinger]

I am a musician and I never thought about that, i really enjoyed the video, more about tuning forks and music/Maths related videos please!!!

[@WhiteSpatula]

I use a set of tuning forks to tune pianos, and from the start I noticed these same properties you discussed here. But I could never wrap my brain around the maths. Awesome explanation, gentlemen! Cheers! -Phill, Las Vegas

[@seanehle8323]

Preamble: I'm the Physics Demonstration Technician at a university. This is so cool! I had to stop the video and grab a tuning fork off the shelf about a third of the way in. I showed dozens of people around the physics department this effect and every one of them thought is was a very cool effect.

[@IceMetalPunk]

This is one of the more elegant, simple, and supremely interesting math/physics facts I've ever seen

[@vivaldirules]

Nicely done. I’m sure I would have puzzled over this a long time and I’m not sure I would have reached that answer. Thank you.

[@viveksoley]

Very impressive. A new bit of information.

[@MAlanThomasII]

The Hz was reading as low by ~1 because you were in a room that was slightly hotter than the standardization temperature, causing thermal expansion of the metal tuning forks, lengthening them and thus lowering the frequency.

[@CasualGraph]

Overtones! Elements of this idea actually show up in Adam Neely's "SUBHARMONIC Music" video, so that may make for an interesting piece of further reading.

[@ryanzarmbinski7446]

That's super cool! I've always wondered why there was an octave difference

[@ysemeniuk]

That was amazing! Thanks!

[@ralfschmelcher9673]

Parker-green at 2:35

[@silkwesir1444]

Parker Color Coding

[@Wecoc1]

3:42 Oh God, the little arrows disappear and reappear again, I will not be able to sleep tonight

[@oisin_smith]

WHERES THE MATT AND HUGH PLAY WITH A THING AND THEN DO SOME MATHS INTRO?

[@matthewbelfield6708]

*then do some working out

[@JBLewis]

I was thinking that they really didn't do enough working out to merit the other intro.

[@eliasabi-elias8501]

What is the app used on his phone?

[@deslomator]

Nice one!

[@bond007rules]

There's some really cool stuff you do with the harmonic series using Fourier transforms and spectrograms which you can do with the human voice. Bit harder to do with other instruments because of the way they're tuned- that's really interesting as well.

[@AnirudhGiri]

Brilliant is the new Audible. Its everywhere!!

[@LetsDark]

Brilliant!

[@macronencer]

So Audible is now inaudible...

[@CaveyRockz]

As a musician I have to voice this fact like others: It IS the same note. You said it yourselves, it's just an octave higher so it's still use the same note name What it is though is a different PITCH which is what directly correlates with the frequency of the vibration. I understand where you're coming from though and it's quite interesting.

[@MyFilippo94]

As a musician I'd like to point out though that composing something out of unison (unisons? Sorry, english is not my first language) is different from using octaves, as a matter of fact. Though classic harmony has a set of rules that limit the same way both consecutive octaves and unison.

[@OliFreke]

Lovely bit of pointless pedantry there! I think these experienced mathematicians know that, and given there's a piano in the background....

[@kfor247]

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.

[@skwisgaarskwigelf5381]

I love this!

[@CoolJosh3k]

‘I never knew you were so good at playing the table”. Please never stop being funny.

[@samuelrj2350]

5:45 "How can the one tuning fork be vibrating at 2 different notes at the same time?" The same way you are able to speak in a voice that's not a singular sine wave. I mean look at the harmonics on the app. It's already vibrating at lots of prominent frequencies. Good stuff, as always :)

[@Bananeisafree]

That is pretty darn fantastic ... The whole relation octave / double the frequency blew my tiny mind ! Cheers!

[@michaelgill6031]

Fascinating! Can you also explain why the ring when you hit the tuning fork is higher than the resonant frequency? For example, my 440Hz fork rings at what seems to be 6x higher (2640Hz, or two octaves and a fifth higher).

[@TheTumshyHeed]

What’s the best iPhone app for trying this out? I’ve got a few but none of them show the dominant frequency in large text as in the video and I like that feature :)

[@klutterkicker]

I recall you using that app for the fidget spinner video, could you tell us what it's called?

[@thijseggen2880]

Hmm, my tuning fork doesn't have that effect it seems. Is that possible? It has an small scoop on the bottom of it, maybe that's compensating the octave change?

[@benjamingeiger]

Which spectrum analyzer app are you using?

[@verdatum]

If you haven't read it yet, "Fundamentals of Musical Acoustics" by Arthur H. Benade was a mindblower for me. Also, how incredible is it that we have excellent oscilloscopes available as free apps on our phones?!? when i was in college, a used device that could come close to this would cost me a couple thousand dollars.

[@guitarmanlevi97]

5:40 Yeah dude it's not going to annoy your musical friends because any decent musician already knows about the overtone series. It was a very nice demonstration of where the higher octave comes from. If you had a spectrometer that showed more than one frequency you would actually be able to see both the frequencies resonating at the same time although the higher octave would be significantly quieter. On most instruments it's common when one note is played for several different multiples of the fundamental to resonate as well. Those are called overtones and are exactly what you just demonstrated. The ear focuses on on the fundamental, but it hears the rest as well. It's what makes a piano playing one note sound different from a guitar or a French horn playing the same note.

[@katnip6289]

Very interesting! I always wanted to buy tuning forks but didn't know how to use them. Where can I buy them and what's the name of that app?

[@lydianlights]

That last demonstration is a cool example of when the subharmonic series actually does appear naturally! You're getting integer divisions of your fundamental instead of multiples.

[@jayantiom2155]

You should do a follow up with weighted tuning forks!!

[@raymantmilnes]

so if you had a tuning fork with 4 prongs would the frequency on the table be 4 times the frequency of when its in the air? or would the frequency be double anyway due to the extra prongs

[@JordanKiener]

Musicians typically won't be surprised you get multiple notes from one fork, as that is the principle of the harmonic series. A vibrating instrument causes notes an octave higher (double the frequency), an octave and a fifth (triple the frequency), two octaves (quadruple) etc. This is how a trumpet is able to play all the notes even though it only has 3 buttons.

[@CreepyMagician]

Regarding the thee-sided coin problem, I will be fascinated to learn that once the optimal ratio is discovered, how it makes sense mathematically (since it appears it will fit neither of the proposed hypotheses).

[@AnthonyFrancisJones]

Forgive me if this is basic and mentioned elsewhere but rotate an oscillating tuning fork around its vertical axis and hear the nodes and antinodes of waves in and out of phase. Great things tuning forks and they have many interesting properties and uses that are not all musical.

[@brachypelmasmith]

how does that simulation work? I mean, if "we" are trying to determine proper ratio for some distribution, what goes into program for expected results?

[@whatelseison8970]

The waveform at the handle wouldn't actually be a sinusoid. It would be more like |sin(wt)|. The motion of the handle is akin to the signal coming from a full-wave rectifier, which is why its fundamental frequency is twice that of the tines, but spectrally it's actually quite different.

[@fdutrey]

How about a standing wave in the tuning forks stem? The stem oscillates up and down and should be tuned in length. I'm thinking standing wave ratio, like an RF antenna. Also, holding the fork introduces a node pretty much at the center (half way) of an already vibrating element. I don't have a tuning fork, but I wouldn't be surprised if by changing the way the fork is held, different results occur. This would inevitably change the ratio between the fundamental and the first harmonic. Maybe holding the fork higher or lower on the stem and/or rotating the stem 90° might yield interesting results.

[@astroflash]

Fab, reminds me of something I discovered years ago and baffled a few people with: Why, if your domestic electricity supply is 50Hz (UK), do your lights flicker at 100Hz? Good luck 😉

[@ColdsideRamrod]

Congrats on committing to the aerodynamic look! I'll be there soon, myself. But still kidding myself that it's not quite thin enough yet...

[@300_WM]

Arthur Weasley finally made it big in the muggle world. So proud of him, way to go man.

[@themasstermwahahahah]

Matt’s hair is BACK!

[@KungFuBlitzKrieg]

Could you have a tuning fork with 3 tongs? And would it then create a pitch other than an octave up when placed on the table?

[@timweber4605]

this can be done with ordinary forks as long as the style of the fork accidentally has a nice tone. It's a cute trick. Pluck a couple of the fork tines to get clear tone holding the fork just off the table. Hold fingers in a pinch near the fork then put your fingers into a glass while setting the end of the fork on the table just as your fingers go into the glass etc. Balancing the fork on a finger and allowing the fork end to barely touch the table will produce a buzz too.

[@b1zzler]

an analogous effect was observed when electro boom and the slow mo guys filmed a tesla cool at a million frames per second- the arcs were strobing at twice the resonant frequency of the tesla coil because both the positive and negative peaks correspond to luminosity peaks in the plasma

[@raindogred]

it looked to be a lot more than 2 frequencies...when you used the spectrum analyser, you could see fundamental, 2nd order, and some of the higher order harmonics as well

[@Yupppi]

I'm not sure if you could annoy the musician friends by saying there's two notes, in musical terms it's the same note in two different octaves, and the original note already contains the harmonic overtone frequency, but the original frequency overpowers it. The demonstration actually shows it pretty nicely where you can see the original frequency and the octave as the strong peaks but different levels when you touch. Also a fun thing to do is touching the ball end of the fork to your skull. Internal loudspeakers.

[@IowaTech80]

What is happening is that you are creating longitudinal waves down the mast as the forks are vibrating in and out, the mast is moving up and down, when you press the butt of the mast against a flat surface it is essentially trading a sustained ring for a shorter amplified ring by transferring the longitudinal waves into the flat surface of the table, like a speaker driver

[@Architector_4]

2 old men hit forks against their hands and then apply them to the table to listen to the sounds.

[@poppet229]

What’s your thoughts of tuning fork on a pole on the schist disc that holds Energy in Egypt their is many tuning forks on poles all different sizes also their is two tuning forks next two each other with string from one to another and every statue has a staff with a tuning fork on the end any thoughts and all hieroglyphics show them as well

[@brettbreet]

I expected a little aside about how air conduction is stronger than bone conduction for humans... so that if you hold the butt of the tuning fork to the bone just behind the ear and wait for the sound to die off, then take it off and listen to the fork "normally", you should be able to hear the note again... though I wonder if the notes also differ by an octave!

[@TheGrundigg]

Adam Neely - The undertone series!

[@fg68at]

Is there a difference between puttin the fork on a table and have it fixed to resonance box?

[@mojosbigsticks]

Go Mirko!

[@ColdFluorescent]

I thought the conclusion would be that as the first tunning fork has a square shape, the vibrations don't flow on a spiral down the fork, making the tone go up an octave when the opposite vibrations combine at the base. With the second fork, the vibrations get to the higher octave at first, but then find their way up and down the fork on the same direction and flowing all in one, keeping the intended frecuency. Just as cilinders can take up more weight than a cube, as the force flows and gets a better distribution. Maybe compare two rounded forks with different bases, to see if that's what's making the vibrations flow steadly?

[@tonhueb429]

Thats a logical explanation. I never noticed that. Went back to check it with my tuning fork and surprisingly it doesn't work. The top part of the fork and the "handle" at the bottom vibrate at exactly the same frequency. (even though I'm a musician, I know how to distinguish between different octaves). Now I'm confused. Can anyone explain this? (I have a smaller tuning fork, similar to the one Hugh showed in the beginning, tuned to 440 Hz, also the "branches" of the fork are more cylinder shaped, not rectangular like in this demonstration.)

[@boyiscola]

Same here, using a small fork with rectangular branches and cylindrical base. 440 Hz from fork and resonance surface.

[@fozzillo]

Same to me with the classic 440Hz small "cylindrical" fork, same octave to the ear and to the app.

[@salvadorbruschy5979]

I tried it too. I never knew the effect happened because my fork produces the same frequency. I double checked it with a tuner, and it is in the same octave, A4. Perhaps what we hear in our ear is the second harmonic and the fork is designed to supress the first.

[@MW-GC]

Thank you so freaking much for using Centripetal instead of Centrifugal. You can only bet on an engineer/physicist to know the difference

[@demonking86420]

Morningwood Gaming isn't the latter not a real force

[@MW-GC]

MichaelKingsfordGray that is not correct. Centripetal force refers to the force pulling the object to a center point. A rope does not provide a pseudo force, and is the Centripetal force in that cenario

[@MW-GC]

Apexfelony yeah Centrifugal is just a product of inertia. It's the extra g's you feel in a spinning wheel

[@HollywoodF1]

Conceptually, centrifugal force is the rotational analogue of normal force. Just as gravitational acceleration can cause a normal force reaction, so can centripetal acceleration cause a centrifugal force reaction. If your problem accepts the limitations of these definitions, your results will be correct. Like many forces, its use a matter of convenience in calculating. Physists can also prove that gravity isn't a force or an acceleration, but is rather a curvature of spacetime. But for convenience, with the proper understanding of limitations of the model, gravitational force will yield correct results.

[@innato4660]

I was not able to reproduce part 1 of this vid: the double frequency when put on the table vertically. The explanation seems logical, but the main frequency stayed the same (i.e. did not double). In the demo, I don't see a real frequency peak in the analyser graph. A pitty because it would have been amazing effect.

[@d34d10ck]

It would be interesting to know what would happen, if you put the fork down on the table at different angles instead of always at 90°. Shouldn't both frequencies crossfade the more you lower the angle?

[@Sgt-Gravy]

Could the property of a tuning fork have anything to do with the effect of the double slit experiment?

[@yuvalne]

As a musician, I'm actually not that surprised that a tuning fork can play different frequencies in different situations. I would have been surprised however, if it wasn't a note which differs by and octave, a fifth or a fourth. Sound waves tend to act strangely, and usually when you hear a note, you're actually hearing many frequencies at once, the higher being a multiple (or near a multiple) of the lowest (that's called the harmonic series). The first intervals in the harmonic series are an octave, then a fifth, then a fourth (an octave above the first one) which is why I expected these changes.

[@arjunpjayakrishnan7271]

Sir, Can you make a vedio on how to piblish a math theorum

[@muazkashif8554]

What is the software that's being used?

[@thesphericalguy9018]

It's funny because at least in my speakers the mics are picking up more of the overtones, it's hard to hear the actual fundamental of the tuning fork unless it's placed on the table.

[@floresaaronj]

What was the app being used?

[@qtheplatypus]

When the note was being displayed there where two side bands next to the main note. Why are ther there?

[@macronencer]

This was great, but I was SO disappointed that the video ended before we heard the /3 pitch :( Did he manage to produce it?

[@MidtownSkyport]

I initially thought it was going to be something to do with the harmonic series, as the surface of the table isn't moving in a perfect sine wave like the fork

[@tsram]

What if you have two forks of same frequency, and then touch their stems together? Depending on the phase, they might either cancel out or double, right?

[@dirtpoorchris]

In my head I just imagine a little gnome hitting a drum every time the tuning pendulum is straight up and down. Im simple.

[@christianaustin782]

So I understand the frequency and centripetal force bit, but why then can't we hear it moving up and down before we put it on the table? Like how does putting it on a surface cause double the frequency to dominate the original frequency?

[@christianaustin782]

Jonathan Love ok that was actually really cool, thanks for sharing! And thanks to wikipedia for filling in the resonance details lol

[@shesoonstar90]

That beautiful wood. WOOD IS MORE SPECIAL THAN WE WILL EVER KNOW.

[@echan101]

mind blown

[@26greg26]

I have a tuning fork that is cylindrical, so it oscillates rotationally, meaning when I put it against a resonant surface the same frequency is produced, not double!

[@srydigital007]

Anyone know what the app is?

[@InTheBeginningTheUniverseWas]

Matt's hair is resisting baldness...? It's come back. Well done Matt's hair, this is impressive.

[@SpencerRaybourne]

Guys, if you ask a musician they will tell you that it is the same note because it IS the same note. What you're doing is the same as if you fretted a stringed instrument at the half way point. You would get the same note different octave. Now can you isolate the overtone series based on the surface you use to amplify the tuning fork?

[@JacobBanerjee2821]

The musical friends who say both notes are the same are still correct, because it is exactly an octave jump, which in music is the same named note, example A4 (440hz) to A5 (880hz) is still called A, even though they are in actave apart

[@turbo3089]

Ty

[@casperdewith]

3:58 That's a really nice photo of Albert Einstein in the background!

[@sebastiangudino9377]

Is that related to the artificial harmonics of the guitar?

[@onehitpick9758]

Hard boundary for internal wave reflection as opposed to soft boundary emphasizes the harmonic. The guitar harmonic selection comment is misleading. Finger positions on a guitar select the primary resonance length and tension, and likewise shift all resonances accordingly as opposed to selecting them.

[@matrixstuff3512]

Lmao simulation with option to turn hair on and off, that's the best

[@EchoHeo]

I love the pen(i almost said where's the brown paper??)

[@soberhippie]

For the fear of being too nerdy about it, but I think I might be in the right place for this, that is the same note. If you go an integer number of octaves from a note, you get the same note, albeit in a different octave.

[@silkwesir1444]

i seem to recall i've heard a word you can stick in front of the word "note" which would make the claim correct. (the same way it would make it correct to switch out the word "note" for "pitch"). can you tell me what that is? intuitively i would go for "exact note", but i may be completely wrong. maybe there isn't even such an expression at all and i'm just misremembering something, or someone told me inaccurate information...

[@nymalous3428]

My brother would like this, not because he likes math, but because he likes music... although, now that I think about it, one of his roommates likes math... (On a different 'note,' I have found that many two-pronged forks, like meat forks or toaster tongs, will act in the same way as a tuning fork, making a tiny tone when struck... just thought some people might find that interesting. [Watch now a bunch of people will be striking their forks to see if they vibrate. Please be careful with the meat forks!])