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Physics of Music, Lecture 11, D. Kirkby 2
MiscellaneousI have added new links to the course web site:
http://positron.ps.uci.edu/~dkirkby/music/html/index.php
where you can check your grades on each problem set and the midterm.
There are also 2 files with the breakdown of the midterm multiple choice section by question.
Problem set #4 is due today. Pick up problem set #5.
Last day to drop this class is Friday.
Physics of Music, Lecture 11, D. Kirkby 3
Review of Lecture 10We discussed how specific frequencies (notes) are chosen to create a musical scale.
We investigated the connection between an instrument’s timbre and the dissonance resulting when two notes are played together on the instrument.
We described pentatonic, diatonic and chromatic subdivisions of an octave. We defined the Pythagorean and Equal Temperament chromatic scales.
Today we will conclude our unit on the perception of sound and start a new unit on the production of musical sound by instruments.
Physics of Music, Lecture 11, D. Kirkby 4
Room AcousticsClose your eyes as you listen to the following samples and try to imagine what kind of space you are in…
The questions we will address today are:
•How does the space you are in modify the sounds that you hear?
•What are the main cues that your brain is using to build its mental model of the space around you?
Physics of Music, Lecture 11, D. Kirkby 5
Direct SoundSound produced at a point will spread out in all directions.
A small amount of this sound will travel directly to your ears. We call this direct sound. I am speaking about 5 meters away from you, so you are hearing my direct sound about (5m)/(345m/s) = 14 ms after I produce it.
The rest of the sound I amproducing travels towardsthe boundaries (walls,ceiling, floor) of this room.
What happens to this sound?
Physics of Music, Lecture 11, D. Kirkby 6
Reflected SoundTwo processes are important when sound reaches the boundaries of your space:
•Reflection (echoes), and•Absorption
Reflection delays theechoes relative to thedirect sound.
Absorption reduces theamplitude of the echoes relative to the direct sound.
When do the echoes arrive at your ear?
Physics of Music, Lecture 11, D. Kirkby 7
Early and Reverberant SoundThe first reflections will make one bounce from the closest surface between the sound source and listener. We call this early sound.
Later reflections will become progressively closer spaced and more absorbed (by multiple reflections). We call this pile-up of many late reflections reverberant sound.Direct sound
Early sound
Reverberantsound
Physics of Music, Lecture 11, D. Kirkby 8
The many reflections that reach your ear in this room result in much more complicated vibrations of your eardrum.
Your brain can detect timing differences between the ears corresponding to a distance of only 10cm. The extra distance traveled by reflections in this room is many meters.
So you should easily be able to resolve the many reflections of my voice reaching your ears. Why aren’t you aware of them?
Physics of Music, Lecture 11, D. Kirkby 9
The Precedence EffectYour brain cleverly masks your perception of the early reflections if they are sufficiently similar in timbre and envelope to the direct sound, and arrive within 50-80ms after the direct sound. This is called the precedence effect.
Early reflections have the potential to disrupt your ability to localize the source of a sound since they generally arrive from different directions than the direct sound.
Amazingly, your brain is able to accurately isolate the direct sound for localization even after many reflections are piled up on top of it.
Physics of Music, Lecture 11, D. Kirkby 10
AbsorptionThere are two limited cases for absorption. In one extreme, the surfaces of the room absorb all the sound that reaches them.
This environment is equivalent to hanging in space, where there are no surfaces to reflect from.
Specially designed rooms calledanechoic chambers approximatethis limiting case using bafflesof absorbing material to lineall surfaces. The lack ofany reflections in an anechoicchamber can be disconcerting!
Physics of Music, Lecture 11, D. Kirkby 11
The other limiting case is an enclosed room with perfectly reflecting surfaces (ie, no absorption).
A room of this type will continue to reflect sound indefinitely. Any sound produced will be stored forever!
Realistic rooms are somewhere between these limiting cases. We can characterize them by:
•The delay between the direct sound and the first early reflection, and
•The time it takes for the reverberant sound to die out (reverberation time).
Physics of Music, Lecture 11, D. Kirkby 12
Reverberation TimeSuppose a perfectly reflecting room has a window that sound can escape through. The reverberation time (RT) for such a room is given by:
RT = 0.161 (Room Volume in m3) / (Window Area in m2)
If instead of a window (which reflects no sound) we have a partially absorbing surface, we can estimate an equivalent window area as:
Equiv. Window Area = (Actual Area) x (Absorption Coefficient)
The equivalent areas of different surfaces add to give a total equivalent window area.
Physics of Music, Lecture 11, D. Kirkby 13
Absorption CoefficientsTables 23.1, 23.2 of the textbook give absorption coefficients for some common surfaces. In general, they depend on the frequency of the sound.
For example, a wood floor has an absorption coefficient of 0.10 at 500 Hz. This means that 10m2 wood floor is equivalent to a 1 m2 window, and would result in a reverberation time of about 3 seconds in a room whose volume is 20m3 (assuming the walls and ceiling are perfectly reflective):
RT = 0.161 (20m3)/(1m2) = 3.22 s
Physics of Music, Lecture 11, D. Kirkby 14
Criteria for Good AcousticsThe ideal room balances size, geometry, and absorption.
A good listening experience requires:•Enough early sound to build perceived loudness without impeding localization
•Enough reverberant sound to envelop the listener from all directions (liveliness), without losing clarity.
The optimum reverberation time is a compromise between loudness, clarity, and liveliness, and depends on the size of the room and its intended use (speech, chamber music, orchestral music, acid rock,…)
Physics of Music, Lecture 11, D. Kirkby 15
Reverberation ExamplesArmed with your new understanding of room acoustics, listen to these examples of speech and short clicks in simulated environments of different sizes:
Clicks Speech
No Reverb.
Small Room
Med. Room
Big Room
Physics of Music, Lecture 11, D. Kirkby 16
The Study of Musical InstrumentsWe are now beginning the third part of the course: a survey of musical instruments.
Our primary goal is to see how the physical principles we learned in the first part of the course are applied in real instruments to produce the full spectrum of musical sounds.
We will study instruments in the following groups:•String•Woodwind•Brass•Keyboard & Percussion•Voice
Physics of Music, Lecture 11, D. Kirkby 17
We will use the following questions to guide our study of each instrument:
•How is it built?•How is energy delivered to the instrument?•What are the resonant systems of the instrument? How are they coupled to the energy source and to each other?
•How are sound waves generated and transmitted beyond the instrument?
•What is the characteristic timbre of the instrument and how is it generated?
•What is the characteristic envelope of the instrument and how is it generated?
Physics of Music, Lecture 11, D. Kirkby 18
String InstrumentsWe will start our study of instruments with the string family, concentrating on the orchestral strings and the guitar.
String instruments generally consist of several strings under tension coupled to a hollow wooden body. Both the strings and the body are resonators.
Energy is delivered by plucking ordrawing a bow across the strings.
Sound waves are mainly produced bythe vibrations of the wooden body,and not by the strings themselves.
Physics of Music, Lecture 11, D. Kirkby 19
The Orchestral String FamilyThere are four instruments in the modern orchestral string family: violin, viola, cello and bass.
The instruments are quite similarin appearance to each other, so wewill concentrate on the violin as arepresentative example from thefamily.
Listen to the samples of eachinstrument playing. How arethey similar? How do theydiffer?
Physics of Music, Lecture 11, D. Kirkby 20
The string-instrument players fill most of the seats in a modern orchestra:
Physics of Music, Lecture 11, D. Kirkby 21
The Construction of a ViolinThe violin, perhaps more than any other instrument, has a lot of mystique surrounding its construction.
Some people believe that the 18th century Italian makers (Stradivari, Guarneri) used secret methods that are unknown today (although most experts would disagree).
In order to understand the physics of a musical instrument, you must know something about how it is built. Here are two photo essays on violin construction:
http://www.vittoriovilla.com/susanna.htm
http://www.vanzandtviolins.com/dvz-resources.htm
Physics of Music, Lecture 11, D. Kirkby 22
The Violin StringsThe strings are the primary resonators.
Orchestral instruments have four strings. Violin, viola and cello strings are tuned to intervals of a fifth (3:2). Bass strings are tuned to a fourth (4:3) to reduced the distance the hand must travel.
Energy is usually delivered to the string by plucking it or drawing a bow across it. In either case, the resonant frequencies of the string correspond to standing waves with a node at both ends.
A string can vibrate at several resonant frequencies at once:
http://id.mind.net/~zona/mstm/physics/waves/standingWaves/standingWaves1/StandingWaves1.html
Physics of Music, Lecture 11, D. Kirkby 23
A Plucked StringA plucked string is initially stretched into a “V” shape:
http://www.phys.unsw.edu.au/~jw/strings.html
What does the string look like some time later, after ithas been released?
Are there any standing waves of the string that will NOTbe excited when it is plucked?Yes: those with a node at the location of the initial pluck.
Physics of Music, Lecture 11, D. Kirkby 24
A Bowed StringBows are made of many strands of horsehair stretched on a wooden stick (usually made from pernambuco wood, found only in a 50 sq.mi. area of Brazil !)
The hair tension is adjusted bytightening or loosening the “frog”.
Physics of Music, Lecture 11, D. Kirkby 25
A bowed string starts out like a plucked string:
http://www.phys.unsw.edu.au/~jw/Bows.html
But there is a difference: the bow stays in contact withthe string after the initial displacement (and all standing waves can be excited).
What does the string look like during its motion when bowed?
Physics of Music, Lecture 11, D. Kirkby 26
The Violin BodyThe body of a violin is a complex resonator with many resonant frequencies.
Remember that there is only one body, but four strings. So the body is not tuned to a particular fundamental, but instead has a rich response over a wide range of frequencies.
The top plate of a violin is made very thin (2-4 mm) in order to vibrate easily. However, the combined force of the 4 stretched strings is equivalent to a weight of about 25 lbs. So the sound post and bass barhidden inside the violin are importantstructural reinforcements (as well asbeing acoustical elements).
Physics of Music, Lecture 11, D. Kirkby 27
The resonant frequencies of the violin body can be grouped into “body modes” and “air modes”.
The front and back plates vibrate together in body modes and so do not displace much air (but still contribute to the instrument’s “feel”).
In air modes, the volume of air changesduring the vibrations and forces air inand out through the “f-holes”. This issimilar to how a bellowsworks.
f-hole
Physics of Music, Lecture 11, D. Kirkby 28
Chladni PatternsThe vibrations of a uniform 2-dimensional plate are difficult to calculate, but relatively easy to visualize experimentally using a technique invented by Ernst Chladni (a father of acoustics and also one of the first people to claim that meteorites fell from space!)
Ernst Chladni (1756-1827)
142Hz
1225Hz
Physics of Music, Lecture 11, D. Kirkby 29
Resonances of the Violin PlatesThe vibrations of a uniform square metal plate are already complicated. What about the front and back plates of a violin with their changing thickness and complicated grain structure?
http://www.phys.unsw.edu.au/~jw/patterns3.html
Physics of Music, Lecture 11, D. Kirkby 30
Is the Bass a Big Violin?The four orchestral string instruments have quite different proportions.
As a result, the matching of the body and string resonances are different in each instrument.
The violin is generally considered to have the best matching and is also the most popular solo instrument.
Physics of Music, Lecture 11, D. Kirkby 31
A New Violin FamilyIn an attempt to reproduce the matching of body and string resonances in lower-pitched instruments, physicists of the Catgut Acoustical Society have been developing a new family of eight string instruments since 1958:
http://www.newviolinfamily.org/
Physics of Music, Lecture 11, D. Kirkby 32
The GuitarThe guitar is an older instrument than the violin, and probably originates from Egypt over 3000 years ago.
The modern guitar usually has six strings tuned to E2, A2, D3, G3, B3, E4 (intervals of a 4th, 4th, 4th, 3rd, 4th).
Physics of Music, Lecture 11, D. Kirkby 33
Guitar ConstructionLike the violin, the guitar has a thin top plate (~2.5mm). The guitar has more substantial structural reinforcement inside its body:
Physics of Music, Lecture 11, D. Kirkby 34
Air escapes from the guitar body through a large round hole under the strings (compare with the violin f-holes).
The guitar neck is fitted with frets to make finger positioning easier.
Guitars are usually plucked (or picked) and not bowed.
Physics of Music, Lecture 11, D. Kirkby 35
Guitar Body VibrationsAt high frequencies, most of the guitar’s sound is produced by vibrations of the thin top plate alone.
At low frequencies, both the top and back plates vibrate to change the volume of air contained in the body, and therefore pump air out through the sound hole.
These images show Chladni patterns for a guitar top plate:http://www.phys.unsw.edu.au/music/guitar/patterns_engl.html
Physics of Music, Lecture 11, D. Kirkby 36
Electric Guitar and BassThe electric guitar and bass usually have solid bodies and so cannot produce a useful amount of sound by string vibrations alone.
Instead, a wire coil (pickup) senses the disturbance of a magnetic field due to the vibrations of the nearby metal string.
The pickup generates anelectronic signal that variesin synch with the motion ofthe string vibrating over it.
http://www.howstuffworks.com/electric-guitar1.htm
Physics of Music, Lecture 11, D. Kirkby 37
Other String InstrumentsThere are many other string instruments that we will not have time to cover…
Physics of Music, Lecture 11, D. Kirkby 38
SummaryWe discussed how reflections and absorption modify the sound you hear, and how the Precedence Effect helps you sort out the complex results.
We completed the second part of this course which dealt with the Perception of Sound, and started the third part which deals with Production of Musical Sound.
We studied the orchestral strings and guitar as examples of the string instruments.
Next, we will discuss woodwind instruments.
