Assignment #4 will be due on Thursday, November 4 in class.
Exercises come from the end of each chapter in the area titled "Exercises." Specific exercises are labeled after the chapter title so that, for example, Exercise 1.3 refers to the third exercise from Chapter 1.
15.4
16.4
17.2
17.4
Thursday, October 28, 2010
Thursday, October 21, 2010
Final Paper
The final research paper must be five to ten pages long. Because this is a research paper, you must use sources that go into more beyond what is covered in the book and in class. (A hint is to look up articles and books on Google scholar.)
The subject of the paper must relate to some aspect of acoustics, specifically the study of vibrations in the physical world or the simulation of vibrations by means of a computer. For example, this can include the study of a particular aspect of an acoustic instrument, how a computer produces a type of sound effect, how our brain processes some specific quality of sound, etc. It is important that the topic be specific enough that your topic is distinct from other students and so that you can go deep into the research of the topic in the confines of five to ten pages. For example, a paper that focuses on all the acoustics of the piano would have to include far more information than five to ten pages can accommodate.
Each student must submit three proposed topics, listed in order of preferences, at the end of class on Thursday, October 28. The assigned topics will be returned in class on Tuesday, November 2.
The final paper is due in class on December 2. Late papers will not be accepted.
Half of the paper's grade will be based upon the paper's style – in other words, that the paper consistently follows a standard research style (e.g. MLA, APA, Chicago, etc. The other half of the grade will based upon the content – does the writing make sense, is it well written and clear, etc.
The subject of the paper must relate to some aspect of acoustics, specifically the study of vibrations in the physical world or the simulation of vibrations by means of a computer. For example, this can include the study of a particular aspect of an acoustic instrument, how a computer produces a type of sound effect, how our brain processes some specific quality of sound, etc. It is important that the topic be specific enough that your topic is distinct from other students and so that you can go deep into the research of the topic in the confines of five to ten pages. For example, a paper that focuses on all the acoustics of the piano would have to include far more information than five to ten pages can accommodate.
Each student must submit three proposed topics, listed in order of preferences, at the end of class on Thursday, October 28. The assigned topics will be returned in class on Tuesday, November 2.
The final paper is due in class on December 2. Late papers will not be accepted.
Half of the paper's grade will be based upon the paper's style – in other words, that the paper consistently follows a standard research style (e.g. MLA, APA, Chicago, etc. The other half of the grade will based upon the content – does the writing make sense, is it well written and clear, etc.
just calc: usage
here's how to derive the ratios from the scale calculator's geometry. sorry if i was unclear about it in person.
to get the ratio of the box you're clicking on, use this formula-
ratio = 1 + (box_number / total_boxes_in_row)
where "box_number" is how many boxes you moved to the right, starting with 0,
and "total_boxes_in_row" is the number of boxes in the horizontal row you've clicked on.
so using this, the top row would contain the ratios 1 (think 2/2) and 3/2 (think 2/2 + 1/2).
the next row down would contain the ratios 3/3, 4/3, and 5/3 . &c...
do you see why the first box will always give us unison (1/1) ?
also, every row with an even number of boxes will give us a ratio of 1.5 somewhere. for the top it's 3/2, for two rows down it's 6/4, four rows down it's 9/6, &c...
let me know if this isn't clear and you'd like it to be.
to get the ratio of the box you're clicking on, use this formula-
ratio = 1 + (box_number / total_boxes_in_row)
where "box_number" is how many boxes you moved to the right, starting with 0,
and "total_boxes_in_row" is the number of boxes in the horizontal row you've clicked on.
so using this, the top row would contain the ratios 1 (think 2/2) and 3/2 (think 2/2 + 1/2).
the next row down would contain the ratios 3/3, 4/3, and 5/3 . &c...
do you see why the first box will always give us unison (1/1) ?
also, every row with an even number of boxes will give us a ratio of 1.5 somewhere. for the top it's 3/2, for two rows down it's 6/4, four rows down it's 9/6, &c...
let me know if this isn't clear and you'd like it to be.
sourcecode for today's demo
here's the sourcecode from today's demo. it's even got our lovely nine-tone just scale! (i swapped out the square wave for our original sine.) hours of entertainment...
a better fm demo
so i wasn't so satisfied with that one-liner i whipped up in class (i can't talk and code at the same time), so i quickly put together this video that will hopefully make things a little more clear. ah, FM... weren't the 80's delightful??
(pedantic side note: to make the math cleaner, i used phase modulation instead of frequency modulation, but the result is identical.)
if you'd like to play with these sounds, download supercollider and copy my example!
some questions to think about (in case you enjoy thinking...):
1) sometimes the resulting spectrum is very harmonic and other times it's very complex. how might this relate to the frequency ratios between the carrier and the modulator? what kinds of ratios might produce a harmonic sound?
2) what effect might the index of modulation have on the spectrum?
3) at what approximate modulator frequency might our perception of the sound shift from a warbly vibrato to a complex spectral phenomenon?
4) jacob mentioned today that ringtones for cell phones often use FM to generate their sounds. why might this be the case?
5) who is john chowning and why is he so darned rich?
(pedantic side note: to make the math cleaner, i used phase modulation instead of frequency modulation, but the result is identical.)
if you'd like to play with these sounds, download supercollider and copy my example!
~fm = {(SinOsc.ar(440, SinOsc.ar(MouseX.kr(1, 2200, 'exponential'))*MouseY.kr(0, 100))*0.5)!2}.play;
some questions to think about (in case you enjoy thinking...):
1) sometimes the resulting spectrum is very harmonic and other times it's very complex. how might this relate to the frequency ratios between the carrier and the modulator? what kinds of ratios might produce a harmonic sound?
2) what effect might the index of modulation have on the spectrum?
3) at what approximate modulator frequency might our perception of the sound shift from a warbly vibrato to a complex spectral phenomenon?
4) jacob mentioned today that ringtones for cell phones often use FM to generate their sounds. why might this be the case?
5) who is john chowning and why is he so darned rich?
Tuesday, October 19, 2010
Video of Today's Demo
Home Lab Group Assignments
Your home lab assignments may be found in this spreadsheet. I'd recommend using your browser's "find" command to locate your name.
Happy noodling!
♤JM
PS - If you can't find your name, you should probably contact us with your preference.
Ring Modulation Patch (HW 7.8)
just intonation scale calculator
click the screenshot for a browser-based demo. (once you calculate a scale, you will not be able to save it unless you download the app.)
this is a simple, geometry-based calculator intended to demystify some of the concepts in just intonation. the boxes correspond to possible notes in a scale, and the vertical lines correspond to positions of equal-temperament tones. these lines are visual guides, and the number of equal-temperament tones per octave is user-adjustable. the ratios become more "complex" (higher value divisor) towards the bottom of the window. to approximate an equal-tempered scale, simply select the number of tones you'd like, select the boxes whose *left* sides most accurately line up with the vertical lines, taking into account the occasional trade-off between simpler ratios and a closer approximation. when you are finished with a scale, you can either clear it by pressing "c" or return it by pressing "r". when the scale is returned, a small text file will be created with the date and time as its title, in the directory of the applet. this file contains the array of ratios you chose using the calculator.
KEYBOARD COMMANDS:
"+" - increase number of vertical bars (tones equal temperament)
"-" - reset number of vertical bars to 2
"c" - clear scale buffer
"r" - return scale buffer, printing to file named with date and time, located in app directory (file io won't work in browser version)
i provide this mostly for didactic purposes, but i also use this personally to obtain some of my scales and i thought it might help other people interested in breaking into microtonal theory.
downloads: OSX WIN LNX
enjoy!
Compositions with beating tones
Here are two compositions where a solo instrument plays against a single sine wave to produce various different beating tones. The composer, Alvin Lucier, frequently makes clear use of acoustic phenomena in his compositions.
The first piece is for clarinet and a sine wave at approximately 280 Hz. Between silences, the clarinet holds steady tones against the tone that are only a few Hz above or below 280 Hz.
The second piece is for cello and a sine wave at approximately 82 Hz. The cello holds steady tones with no vibrato against the tone that are only a few Hz above or below 82 Hz. Note how big the standing waves are in space and how hard it can be to find an optimal listening position. Also notice, how quiet instrument is. You can usually notice the beating before you notice the instrument's timbre.
Alvin Lucier:
Still and Moving Lines in Families of Hyperbolas
#1 for clarinet
#11 for violoncello
The first piece is for clarinet and a sine wave at approximately 280 Hz. Between silences, the clarinet holds steady tones against the tone that are only a few Hz above or below 280 Hz.
The second piece is for cello and a sine wave at approximately 82 Hz. The cello holds steady tones with no vibrato against the tone that are only a few Hz above or below 82 Hz. Note how big the standing waves are in space and how hard it can be to find an optimal listening position. Also notice, how quiet instrument is. You can usually notice the beating before you notice the instrument's timbre.
Alvin Lucier:
Still and Moving Lines in Families of Hyperbolas
#1 for clarinet
#11 for violoncello
Thursday, October 14, 2010
Homework # 3
Assignment #3 will be due on Thursday, October 21st in class.
Exercises come from the end of each chapter in the area titled "Exercises." Specific exercises are labeled after the chapter title so that, for example, Exercise 1.3 refers to the third exercise from Chapter 1.
8.2
8.6
9.8
Exercises come from the end of each chapter in the area titled "Exercises." Specific exercises are labeled after the chapter title so that, for example, Exercise 1.3 refers to the third exercise from Chapter 1.
8.2
8.6
9.8
Roughness and beats demo
Here is a recording of the demo from 10/14.
http://www.music.mcgill.ca/~jacob/acoustics/sweep.mp3
A steady tone sounds at 571 Hz while a second sine waves goes from 520 Hz to 620 Hz over the course of about 2 minutes. Listen for the moment when the roughness begins, when the beats begin, and so on.
http://www.music.mcgill.ca/~jacob/acoustics/sweep.mp3
A steady tone sounds at 571 Hz while a second sine waves goes from 520 Hz to 620 Hz over the course of about 2 minutes. Listen for the moment when the roughness begins, when the beats begin, and so on.
Thursday, October 7, 2010
Home Lab Assignment
Home Lab (HL) preference – due Thurs. 10/14/10
Read description of the “Experiments for Home, Laboratory and Classroom Demonstration” at the end of chapters 1-7.
Experiments can be done in pairs, so choose your partner or small groups of three or four.
Choose 3 experiments and rank them according to your preferences (1 highest – 3 lowest).
Submit a list of HL preferences with all the members' names on it.
We will try to sort out your list so as to accommodate as many preferences as possible.
On Th. (10/21) evening we will publish the final HL assignments
(check email / see web link below).
HL are due Tuesday 10/26/10 (one weeks) as a presentation in class during approx. 10 min.
Presentation should include a one page written description of the experiment.
Also prepare a separate page only with your names and the Lab title on it
Read description of the “Experiments for Home, Laboratory and Classroom Demonstration” at the end of chapters 1-7.
Experiments can be done in pairs, so choose your partner or small groups of three or four.
Choose 3 experiments and rank them according to your preferences (1 highest – 3 lowest).
Submit a list of HL preferences with all the members' names on it.
We will try to sort out your list so as to accommodate as many preferences as possible.
On Th. (10/21) evening we will publish the final HL assignments
(check email / see web link below).
HL are due Tuesday 10/26/10 (one weeks) as a presentation in class during approx. 10 min.
Presentation should include a one page written description of the experiment.
Also prepare a separate page only with your names and the Lab title on it
Homework 2
Assignment #1 will be due on Thursday, October 14th in class.
Exercises come from the end of each chapter in the area titled "Exercises." Specific exercises are labeled after the chapter title so that, for example, Exercise 1.3 refers to the third exercise from Chapter 1.
5.2
5.4
6.2
6.6
7.2
7.4
7.8
Exercises come from the end of each chapter in the area titled "Exercises." Specific exercises are labeled after the chapter title so that, for example, Exercise 1.3 refers to the third exercise from Chapter 1.
5.2
5.4
6.2
6.6
7.2
7.4
7.8
Monday, October 4, 2010
Homework Deadline Delay
Due to problems with the bookstore receiving the textbook, we've decided to delay the due date of the first assignment until Thursday. All future assignments will be due on Thursday.
If you don't yet have the textbook, it might be recommended to buy it from some other online source which has cheaper prices than the UCSD bookstore.
If you don't yet have the textbook, it might be recommended to buy it from some other online source which has cheaper prices than the UCSD bookstore.
Sunday, October 3, 2010
Example of Resonance at Work
Here's a video of the Tacoma Narrows Bridge that collapsed because it was built of a single piece that could resonate when activated by the wind. It's a nice way to see the resonant modes at work.
A Few Useful Formulas
//===============
//Chapter 1:
//===============
v = d / t
a = v / t
F = ma
p = F⊥ / A
W = Fd
W = mgh
KE = (1/2)mv²
PE = mgh
PE = (1/2)Ky²
PE = (1/2)(V/P₀)p²
PE = (2T / L)y²
Ƥ = W / t
//===============
//Chapter 2:
//===============
ƒ = 1 / T
ƒ = (1/2π)√(K/m)
KE = (1/2)mv²
PE = (1/2)Ky²
ƒ = -Ky
ƒ = (1/2π)√(g/l)
ƒ = (1/2π)√(ΥpA/ml)
ƒ = (v/2π)√(a/Vl)
m = ρal
K = ρa²v² / V
V = (4/3)πr³
ƒª = (1/2π)√(K/m)
ƒᵇ = (1/2π)√(3K/m)
//===============
//Chapter 3:
//===============
v = ƒλ
v = √(E/ρ)
v = √(T/μ)
v = √(ΥRT/M)
ƒ'= ƒs ((v+v₀)/v)
ƒ = ƒs (v/(v-vs))
//===============
//Chapter 4:
//===============
Q = ƒ₀/Δƒ
ƒn = n (v/2L) = nƒ₁
ƒn = (n/2L)√(T/μ)
ƒn = (n/2L)√(E/ρ)
//===============
//Appendix 10:
//===============
y = AsinΦ = Asin360(t/T)
sin = opposite / hypotenuse
coh = adjacent / hypotenuse
tan = opposite / adjacent
//Chapter 1:
//===============
v = d / t
a = v / t
F = ma
p = F⊥ / A
W = Fd
W = mgh
KE = (1/2)mv²
PE = mgh
PE = (1/2)Ky²
PE = (1/2)(V/P₀)p²
PE = (2T / L)y²
Ƥ = W / t
//===============
//Chapter 2:
//===============
ƒ = 1 / T
ƒ = (1/2π)√(K/m)
KE = (1/2)mv²
PE = (1/2)Ky²
ƒ = -Ky
ƒ = (1/2π)√(g/l)
ƒ = (1/2π)√(ΥpA/ml)
ƒ = (v/2π)√(a/Vl)
m = ρal
K = ρa²v² / V
V = (4/3)πr³
ƒª = (1/2π)√(K/m)
ƒᵇ = (1/2π)√(3K/m)
//===============
//Chapter 3:
//===============
v = ƒλ
v = √(E/ρ)
v = √(T/μ)
v = √(ΥRT/M)
ƒ'= ƒs ((v+v₀)/v)
ƒ = ƒs (v/(v-vs))
//===============
//Chapter 4:
//===============
Q = ƒ₀/Δƒ
ƒn = n (v/2L) = nƒ₁
ƒn = (n/2L)√(T/μ)
ƒn = (n/2L)√(E/ρ)
//===============
//Appendix 10:
//===============
y = AsinΦ = Asin360(t/T)
sin = opposite / hypotenuse
coh = adjacent / hypotenuse
tan = opposite / adjacent
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