Physics of a 2 litre Bottle

BossArky

Hello,
Currently I'm studying Music Technology and I am looking for information relating to the physics of a 2 litre bottle, e.g. a coke or 7-up bottle...or a flagon of cider.
My acoustics project involves designing a musical instrument from household items and then producing the proper Mathematical and Physical formulae to state why this instrument produces certain frequencies or sounds.
Any ideas where I find information on these formulae? How can I work out the Physics of a 2-litre bottle?
Thanks.

Woden

All i can say is good luck to you, my first piece of advice would be to ditch the coke bottle anything with curves like that is going to make things more difficult, the more symmetry the bottle has the easier it will be. Another thought would be would be anything your interested in will be related to the length of the bottle, could it be something to do with resonance in the bottle with certain forms of standing waves being produced, i recall an experiment in school to measure the speed of sound and it involved a long narrow tube and was related to standing waves

P.S maybe contact the mathematical physics department in u.c.d perhaps they could help?

DadaKopf

You might also try to get in touch with an acoustic engineer - y'know, the fellas who make sound studios. They know a thing or fifty about how sound works in spaces, no matter how small.

Contact Windmill Lane studios, for example.

Gordon

We used to have a tumble dryer that had a very cool springy pipe that you fitted to it and pulled it out the window so that the moist air would blow outside. If you took a flat plank of wood and hit it over one end it would make a note out the other end. Now depending on how long you stretched it the note would get deeper... maybe. I didnt actually try it but the mathematics involved would be much less.. involved. Not that I condone taking the easy way out

hmm... /me wanders off thinking about a cool bassline

Oh and I doubt Windmill Lane recording studios would help you out in that way.

OSiriS

I would have thought theory of acoustics would be an integral part of the course .. or were you asleep for that lecture?;P

BossArky

Actually, this experiment / project is for my Acousitcs module...its a kind of sink or swim thing...they gave us the project about 2 months ago and said "do it"...its up to us to learn what we want...not too much spoon feeding.

Figured out the Maths last night...

something like:

f= 2c/pie(root(s/vl))

f = frequency of note
c = speed of sound in medium(air)
pie=3.14
root = square root, duh.
s=cross section width of neck of bottle
v= volume of container free..e.g. full of air..2 litres.
l=length of neck approximately.

"G" of about 24 Hertz is produced by blowing across the top of an empty 2 litre....or thats what the numbers tell me...and I can tune my guitar to it

Gordon

24 Hz?!! You sure that's correct? Human hearing just about goes down to 20Hz if you are of perfect ear. That's almost subsonic.

Anyway isn't 24Hz just below F?

daveirl

This post has been deleted.

Gordon

My calculator tells me 2 litres = 0.070622 cubic feet.

... my brain tells me that it hurts already.

Oh and a 2 litre bottle of pop (ahh I like that word *pop*) is a wee bit over 2 litres remember. 2 Litres will be the quantity of *pop* but slightly over that is the actual capacity.

BossArky

NOTE FREQUENCIES (Hz)
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| OCTAVE |
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|NOTE | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
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| A |27.5| 55.0|110.0|220.0|440.0| 880.0|1760.0|3520.0| 7040.0|
|A#/Bb|29.1| 58.3|116.5|233.1|466.2| 932.4|1864.7|3729.4| 7458.9|
| B |30.9| 61.7|123.5|247.0|493.9| 987.8|1975.7|3951.3| 7902.7|
| C |32.7| 65.4|130.8|261.6|523.3|1046.6|2093.2|4186.5| 8372.9|
|C#/Db|34.6| 69.3|138.6|277.2|554.4|1108.8|2217.7|4435.5| 8871.1|
| D |36.7| 73.4|146.8|293.7|587.4|1174.8|2349.7|4699.5| 9398.9|
|D#/Eb|38.9| 77.8|155.6|311.2|622.4|1244.8|2489.5|4979.1| 9958.1|
| E |41.2| 82.4|164.9|329.7|659.4|1318.8|2637.7|5275.3|10550.6|
| F |43.7| 87.3|174.7|349.3|698.7|1397.3|2794.6|5589.2|11178.4|
|F#/Gb|46.2| 92.5|185.1|370.1|740.2|1480.4|2960.8|5921.8|11843.5|
| G |49.0| 98.0|196.1|392.1|784.3|1568.2|3137.1|6274.1|12548.2|
|G#/Ab|51.9|103.9|207.7|415.5|830.9|1661.9|3323.7|6647.4|13294.8|
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the 2 litres volume has been taken into account...the volume in the formulae is from beneath the neck of the bottle.

I tried it for C sharp and it was a bit out...have 12 flagon bottles here...all with varying amounts of water...G to F sharp....thing the maths is correct...just have to fiddle a bit more with the exact cross section, etc.

yes human hearing is 20 - 20k Hertz ...I'm assuming that my hearing is ok...

are you sure that it should be cm3?./....I was thinking litres..what is the conversion ratio between them?

Gordon

Apologies BossArky, I was looking at the wavelength of sound in nanometres (little ongoing project of mine).

Good luck

Woden

To get a value in Hertz you need to work in S.I use m^3 for volume not litres not cubic centimetres

Woden

P.S any chance you can post the derivation or mail it to me?

daveirl

This post has been deleted.

Gordon

Yeah cubic feet. I don't even know how big a foot is, I got a pair of shoes today (get this) and the pair I was wearing was a 9 and I ended up buying a pair of 7s!! Whats with that? I can understand one size being different for maybe US-Euro but 2?

Anyway, yea the cubic feet thing is because I have a nifty calculator that translates litres into feet3 and US gallons drams pints and more alcoholic sizeables. what are we living in now the centimetre age or the pint age?

Woden

hi just taking what i considered to be typical value for your formula of

f=2*c/pie*(s/v*L)^1/2

c=340*m*s^-1
pie=3.14
s=pie*(0.01)^2 assuming a radius of 1cm for the bottle neck giving the C.S.A of s
v=2litres=2/1000 m^3
L=3cm

??

i get about 94.6 for the frequency, but thats just pure guesstimation

BossArky

Hmmmm...

I used my initial values for the 2 litre bottle again.

Since speed of sound is dependent on air temp I used the following formula to work out "c":

c = 331.4 + 0.6(Temp in Celcius).... it was 21 Deg C ...so c = 344m/s.

Pie = 3.14

S = only 0.022 of a metre...why did you multiple it by pie and square it...that is not necessary...it is only a straight measurement.

V = 2/1000 m3 following the advice given...but I think this is incorrect as I ended up with a Frequency value of 700!!....which is definetly way too high for what this bottle is producing.

L = neck length...plus I found physics links to "Helmholtz Resonators"...it says to add on 0.6 of the width of neck at one end, plus the full length of the neck at the other end....so since my bottle neck is all the same I get 0.032 + 0.0132 + 0.022 = 0.0672. .......they are all in metres..

so subbing in etc I get 700, which is almost an F...but a very high one.


are you sure about that metres cubed thing in the volume?

Woden

i thought it was cross sectional area of the bottle top so i used
pie*radius^2, if you want a value in hertz the volume is definitely metres^3 and as far as i know the conversion from litres to metres^3 is division by a thousand but i may be incorrect, i gonna try subbing the units for your formula in a a program to see if it gives me Hz or s^-1 as that is important.

Woden

ok putting the units into the formula i got f to have units of m^0.5*s^-1, this happened regardless of whether the unit of volume was litres or m^3 and using a cross section not a cross sectional area.

using a cross sectional area the unit for f was m*s^-1

either way it isnt the unit for frequency, so perhaps there is something fundamentally flawed with the formula?

Ciaran

The units for that formula aren't right for a start. I would have thought that the CSA and length of the main part of the bottle would matter too.

BossArky

its ok...got it working last night...I hope for the last time..

yeah it is the cross sectional area of the bottle neck....

and the volume is in metres cubed...so that division by 1000 is correct.....

the length of the whole bottle dosen't matter...just the volume of free space in it.

Proved it for G1 and C2...will do the rest later.

Woden

Did all the units cancel then go give you s^-1? does the original formula you had still apply with out the length in it?

BossArky

are you in my class?

Woden

nah i study science

thedrowner

he's in my class though!!!

Woden

hello drowner, saw your post about the buses too, shocking you have way too much free time on your hands