A C O U S T I C S of W O O D
Jan Tippner, Dep. of Wood Science, FFWT MU Brno
jan.tippner@mendelu.cz
Lecture 1
A C O U S T I C S of W O O D
Lecture 1
Very brief preface:
Acoustics – The field of Physics
interdisciplinary, study of sound, ultrasound and infrasound (mechanical waves in gases, liquids, and solids), hearing = crucial means > acoustics spreads across music, medicine, architecture, industrial production, warfare etc., Greek „akoustikos“ meaning "of or for hearing, ready to hear",
… but refer to the entire frequency range without limit.
Wood – Material (not only …)
superb material used in large range of applications... src: www.jvc.com
anisotropic, viscoelastic, multicomponent, inhomogeneous and hygroscopic;
fibre­composite material consists of cellulose fibres in a lignin matrix; has strong anisotropy (about 90 to 95% of all the cells are elongated and vertically ordered) ­ in orthogonal directions: generally considered as orthotropic material (L, R, T); viscoelastic behavior ­ lignin matrix; all the major components (cellulose, hemicelluloses and lignin) are polymers,... properties of wood – (dynamics, acoustics).
(… Natural frequencies and modes of soundboard, Influence of moisture to sound speed of wood,
Determination of dynamical moduli of elasticity and internal damping of wood ...)
A C O U S T I C S of W O O D
Lecture 1
Content of lecture 1:
1. Introduction to the course: how to pass the course successfully.
2. Contents of acoustics and acoustics of wood.
(topics, domains of acoustics) 3. Theory background of acoustics.
(sound, propagation, frequency, amplitude ...)
A C O U S T I C S of W O O D
Lecture 1
Content of lecture 1:
1. Introduction to the course: how to pass the course successfully.
2. Contents of acoustics and acoustics of wood.
(topics, domains of acoustics) 3. Theory background of acoustics.
(sound, propagation, frequency, amplitude ...)
A C O U S T I C S of W O O D
Lecture 1
See „UIS“... http://is.mendelu.cz
ECTS­credits: 5
Objectives and contents – 13 weeks
Student will be introduced to acoustics with orientation to properties of wood and utilization of wood. Course consists of the topics: theory of acoustics, wave propagation in the wood, dynamical and acoustical properties of different wood species, internal friction in the wood, experimental methods for the acoustic characterization of wood, sound as nondestructive tool for wood characteristics assessment, influence of aging and moisture in the acoustic properties of the wood, methods for improving acoustic properties of wood, acoustic emissions, room acoustics, acoustics of musical instruments, numerical methods in vibro­
acoustics, using of wood in architecture, sound reproducer systems and musical instruments.
Learning methods
Lectures and practicals: 39 hours
Home studies, preparation for exam: 30 hours
Total workload: 69 hours
Assessment
Written exam
A C O U S T I C S of W O O D
Lecture 1
Syllabus of the Course:
Week No. 2 ­ Wave propagation in the wood. Dynamical and acoustical properties of different wood species.
Week No. 3 ­ Damping, internal friction in the wood.
Week No. 4 ­ Laboratory: frequency analysis of wooden bar, determination of logarithmic decrement of damping in the wood.
Week No. 5 ­ Experimental methods for the acoustic characterization of wood. Sound as non­destructive tool for wood quality assessment.
Week No. 6 ­ Laboratory: determination of sound velocity in the wood, determination of dynamic elastic moduli in the wood.
Week No. 7 ­ Influence of aging to acoustic properties of wood. Influence of moisture to acoustic properties of wood. Improving of acoustic properties of wood. A C O U S T I C S of W O O D
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Syllabus of the Course:
Week No. 8 ­ Revision, short test. Acoustic emissions, room acoustics, sound reverberance. Wood, acoustics & architecture.
Week No. 9 ­ Acoustic of musical instruments. Week No. 10 ­ Modal analysis , harmonic analysis and acoustic analysis by the help of finite element method.
Week No. 11 ­ Laboratory: determination of natural frequencies of soundboards, Chladni's patterns of vibration of soundboard.
Week No. 12 ­ Wood & sound reproducer systems.
Week No. 13 ­ Written exam.
A C O U S T I C S of W O O D
Lecture 1
Literature:
Bader, R., Computational mechanics of the classical guitar. 1. vyd. Berlin: Springer, 2005. Berthelot, J., Composite Materials: Mechanical Behavior and Structural Analysis. New York: Springer Verlag, 1998. ISBN 0­387­98426­7. 3­540­25136­7.
Bodig, J., Jayne, B., A., Mechanics of Wood and Wood Composites. Malabar: Krieger Publish.Comp., 1993. ISBN 0­89464­777­6.
Bucur, V., Acoustics of Wood. Boca Raton: CRC Press, 1995. ISBN 0­8493­4801­3.
Bucur, V., Nondestructive characterization and imaging of wood. Berlin: Springer, 2003. Springer series in wood science. ISBN 3­
540­43840­8.
Bröker, F.­W., Proceedings of the 14th International Symposium on Nondestructive Testing of Wood : May 2 ­ 4, 2005, University of Applied Sciences Eberswalde, Germany. Aachen: Shaker, 2005. ISBN 3­8322­3949­9.
Frýba, L., Vibration of solids and structures under moving loads. Prague: Academia, 1999. ISBN 80­200­0715­6.
Gandra, M., World Musical Instruments : Musikinstrumente der Welt. 1. vyd. Amsterdam: Pepin Press, 2008. ISBN 978­90­5768­116­5.
Irudayaraj, J., Nondestructive testing of food quality. Ames, Iowa: Blackwell, 2008. IFT Press series. ISBN 0­8138­2885­6.
A C O U S T I C S of W O O D
Lecture 1
Literature:
Mechel, F. P., Formulas of Acoustics, Springer, 2002, ISBN 3­540­42548
Nondestructive evaluation and flaw criticality for composite materials. Philadelphia: American Society for Testing and Materials, 1979.
Nondestructive evaluation of wood. Madison: Forest Products Society, 2002. ISBN 1­892529­26­2.
Proceedings of the 13th international symposium on nondestructive testing of wood : August 19­21, 2002, University of California, Berkeley Campus California, USA. Madison: Forest Products Society, 2003. ISBN 1­892529­31­9.
Riley, W., F., Sturges, L., D., Engineering Mechanics: Dynamics. New York: John Wiley & Sons, 1993. ISBN 0­471­
51242­7.
Schanz, M., Wave propagation in viscoelastic and poroelastic continua: a boundary element approach. Berlin: Springer, 2001. Lecture notes in applied mechanics. ISBN 3­54041632­3.
Tondl, A., Quenching of Self­Excited Vibrations. Prague: Academia, 1999. ISBN 0­444­98721­5.
Zienkiewicz, O.,C., Taylor, R., L., The finite element method: Basic formulation and linear problems. London: McGraw­Hill, 1989. ISBN 0­07­084174­8.
Zienkiewicz, O.,C., Taylor, R., L., The finite element method: Solid and fluid Mechanics, dynamics and non­linearity. Berkshire: McGraw­Hill, 1991. ISBN 0­07­084175­6.
A C O U S T I C S of W O O D
Lecture 1
Content of lecture 1:
1. Introduction to the course: how to pass the course successfully.
2. Contents of acoustics and acoustics of wood.
3. Theory background of acoustics.
A C O U S T I C S of W O O D
Lecture 1
History …
Pythagoras ­ maybe the first person studying the relation of string lengths to consonance. Why some intervals seemed more beautiful than others?!
… and he found answers in terms of numerical ratios representing the harmonic overtone series on a string.
Medieval woodcut showing... e.g. Pythagoras with bells in Pythagorean tuning
A C O U S T I C S of W O O D
Lecture 1
… history …
The Chinese were already using a scale based on the knotted positions of overtones that indicated the consonant pitches related to the open string (3000 BC).
Aristotle (384­322 BC) ­ sound consisted of contractions and expansions of the air "falling upon and striking the air which is next to it...". Roman architect and engineer Vitruvius wrote a treatise on the acoustic properties of theatres including discussion of interference, echoes, and reverberation—the beginnings of architectural acoustics (cca 20 BC).
The fundamental and the first 6 aliquotes of a vibrating string. A C O U S T I C S of W O O D
Lecture 1
... history …
Galileo (1564–1642) and Mersenne (1588–1648) independently discovered the complete laws of vibrating string, also beginnings of physiological and psychological acoustics. Galileo Galilei: "Waves are produced by the vibrations of a sonorous body, which spread through the air, bringing to the tympanum of the ear a stimulus which the mind interprets as sound"
Experimental measurements of the speed of sound in air were carried out successfully between 1630 and 1680
by a number of investigators, prominently Mersenne.
Newton (1642–1727) derived the relationship
for wave velocity in solids, a cornerstone of physical acoustics (Principia, 1687).
Adapted scetch from Newton's Principia – passage of waves trough the hole. A C O U S T I C S of W O O D
Lecture 1
… and the history.
18th century ­ major advances in acoustics at the hands of the great mathematicians with the new techniques of the calculus (wave propagation theory). 19th century Helmholtz (Germany) elliptic partial differential equation ­ relations of wavenumber and amplitude Helmholtz resonator based on his original design cca 1890­1900, src: wikipedia.
19th century Lord Rayleigh (England) ­ monumental work "The Theory of Sound". Also Wheatstone, Ohm, and Henry developed the analogy between electricity and acoustics.
20th century ­ technological applications like Sabine’s work (architectural acoustics) etc. (… underwater acoustics was used for detecting submarines, sound recording, telephone, sound measurement and analysis through the use of electronics and computing, ultrasonic frequency in medicine and industry, new transducers...)
A C O U S T I C S of W O O D
Lecture 1
Main Domains of Acoustics:
1. Physical acoustics
2. Biological acoustics
3. Acoustical engineering
by R. Bruce Lindsey (J. Acoust. Soc. Am. V. 36 ­ 1964). 4 broad fields of Earth Sciences, Engineering, Life Sciences, Arts. The outer circle ­ disciplines one may study to prepare for a career in acoustics. The inner circle ­ various disciplines naturally lead to.
17 major subfields, ­ by Physics and Astronomy Classification Scheme® (PACS®) src: http://publish.aps.org/PACS
A C O U S T I C S of W O O D
Lecture 1
Domains of Acoustics:
Physical acoustics Aeroacoustics
General linear acoustics
Nonlinear acoustics
Structural acoustics and vibration
Acoustical engineering
Biological acoustics
Bioacoustics
Musical acoustics
Physiological acoustics
Psychoacoustics
Speech communication Acoustic measurements and instrumentation
Acoustic signal processing
Architectural acoustics
Environmental acoustics
Transduction
Ultrasonics
Underwater sound
Room acoustics
17 major subfields, ­ by Physics and Astronomy Classification Scheme® (PACS®) src: http://publish.aps.org/PACS
A C O U S T I C S of W O O D
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:­)
A C O U S T I C S of W O O D
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What is the Acoustics of Wood? ... application of acoustics in wood science, wood industry? wood as material – properties, modifications, measurements and mat. characterization, propagation of waves
forests and forest products (environmental noise, grading or treatment of products)
constructions: wooden musical instruments (violins, guitars, pianos, woodwinds – problems of natural aging, environmental conditions, long term loading, varnishing) and buildings (insulators, wooden acoustic panels, concert halls)
NDT (from germinability detection of acorns to trees, timbers, lumber grading, wood products, wooden composites etc.– defects, quality, properties)
acoustic emission – diagnostics (biological agents, fracture mechanics, monitoring of technological processes – wood machining, drying of lumber, adhesives, structures)
acoustical treatment (high­energy ultrasonic modifications, drying, defibering, cutting, plasticizing, regeneration on aged glue resins, improving wood preservation, wood sterilization etc.)
A C O U S T I C S of W O O D
Lecture 1
Content of lecture 1:
1. Introduction to the course: how to pass the course successfully.
2. Contents of acoustics and acoustics of wood.
3. Theory background of acoustics.
A C O U S T I C S of W O O D
Acoustics study the sound – the generation, propagation and reception of mechanical waves.
The fundamental steps can be found in any acoustical event or process.
Lecture 1
CAUSE
GENERATION
In fluids, sound propagates primarily as a pressure wave. In solids, mechanical waves can take many forms including longitudinal waves and transverse waves.
PROPAGATION of WAVE
RECEPTION
EFFECT
Numerical simulation of 8th natural mode of wooden beam
A C O U S T I C S of W O O D
Lecture 1
In transverse waves, the movement of the elements of the medium move orthogonally (at 90°) to the direction of movement of the wave. A typical example of a transverse wave is a wave pattern on the surface of a body of water (eg. on a pond after a stone has been thrown in or ocean waves before they reach the breaking zone). In figure hand induces a transverse wave in a string by periodically moving up and down. This movement propagates through the string producing a series of wavefronts which move towards the fixed wall with a velocity v. Obviously, individual parts of the string only move up and down (as indicated by the vertical arrows).
A C O U S T I C S of W O O D
Lecture 1
In longitudinal waves the elements of the medium move back and forth in line with the direction of propagation of the wave fronts.
In figure a hand induces a longitudinal wave in a spring by periodically moving back and forth in line with the direction of the spring. This causes the regions of high and low spring compression to move along the spring. This movement propagates through the spring producing a series of wavefronts which move towards the fixed wall with a velocity v. Individual parts of the spring only move backwards and forwards short distances in the direction of wave propagation. A C O U S T I C S of W O O D
Lecture 1
What is sound?
­ it's a longitudinal compression wave, mechanical wave of energy that changes the pressure of its medium as it moves; these changes of pressure are detected by our sense of hearing and transmitted to our brains for interpretation; sound waves are described by their wavelength (m), frequency (Hz) and intensity ­ amplitude (e.g. in dB)
­ is caused by something vibrating (without vibration there is no sound) ­ in this way a disturbance of the air moves out from the source of the sound and may eventually reach the ears of a listener.
­ the simple way to understand the propagation of sound is through the example of human speech; the sound (tone, noise ...) is created at the source by the compression and decompression of air particles by the diaphragm action of the voice box which creates a sound pressure wave through the atmosphere; the ear (the receiver) in turn has a diaphragm which detects the vibration of the air pressure changes and transmits this to the brain, which turns it into intelligible speech.
A C O U S T I C S of W O O D
Lecture 1
Sound propagation, reflection, absorption, transmision, reverberation
­ when a sound is propagated in a source room a sound pressure wave is created which moves out from the source of the sound, gradually dissipating as it moves further from the source
­ the sound will continue to reflect off the hard wall, floor and ceiling surfaces until it loses energy and dies out ­ the prolongation of reflected sound is known as reverberation (Reverberation Time is defined as the number of seconds it takes for the reverberant sound energy to die down to one millionth ­ or 60 dB of its original value from the instant that the sound signal ceases)
­ reverberation is dependant only on the volume of a space and the acoustically absorptive quality of the rooms finishes. Hard surfaced rooms will have a longer reverberation time than rooms finished with sound absorbing materials
­ sound will therefore be dissipated in three ways in varying degrees depending upon the acoustic characteristics of the room. These are reflection, absorption and transmission.
A C O U S T I C S of W O O D
Lecture 1
Flashback
­ sound is a wave motion that carries energy from one point to another, ­ the medium through which the sound wave travels will be air, although sound can also travel through solids and liquids ­ the "wave" itself consists of very small pressure fluctuations in the air about the ambient (atmospheric) pressure ­ at some points along the sound wave, the air pressure is slightly above the ambient level (the air is compressed), and at others it is below (the air is rarefied)
­ these compressions and rarefactions are generated by the source of the sound wave, usually a vibrating object such as a violin string, a loudspeaker...
­ sound velocity in air depends on atmospheric pressure and temperature, with the latter being the more significant factor; the velocity at 0°C is 332 metres per second, rising by 0.6 metres per second for each °C increase in temperature
­ the amplitude of the pressure fluctuations in the sound wave (how far they are above and below the ambient pressure) determines how loud the sound is, while the frequency of the pressure fluctuations (how rapidly they change from above to below the ambient pressure) determines its pitch
A C O U S T I C S of W O O D
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1. About Amplitude (Loudness vs. Amplitude vs. Intensity)
­ is measured by the strength of the sound, depicted as a sine wave above and below the normal atmospheric pressure (101325 Pa), the basic unit of sound pressure is the pascal Pa – N/m2 , bars etc. ­ the greater the pressure change, the louder the sound, humans are sensitive to a remarkably wide range of sound pressure amplitudes (about 1 million to one)
­ the ear is capable of detecting a pressure change as small as 0.0002 microbar, one microbar is equal to one millionth of atmospheric pressure, the threshold of pain is around 200 microbars
­ the sound pressure that is only just perceivable (ie. the threshold of hearing for a 1000 Hz tone) is taken to be 2x10­5 Pa (20 µPa) ­ so called Standard Reference Sound Pressure Level (SPL)
­ actual threshold of hearing varies greatly from frequency to frequency as well as from person to person
­ actual sound pressure involved is about 1/5,000,000,000 atmospheric pressure >>> it is common to quote sound pressure in µPa
A C O U S T I C S of W O O D
Lecture 1
1. About Amplitude (Loudness vs. Amplitude vs. Intensity)
­ the threshold of pain (ie. the maximum sound pressure that can be perceived without pain) is about 100 Pa or about 1/1000 atm, which is 5,000,000 times the threshold sound pressure
­ thresholds have also been defined in terms of intensity, with the standard intensity threshold of hearing being: 10­12 Watts.m­2 ­ so called Standard Reference Sound Intensity
­ the intensity of a sound, with a sound pressure level of 20 µPa, is very close to 10­12 W/m2
­ the intensity of a sound is proportional to the square of the sound pressure: I =P
2
­ at 1 atm and 20°C approx. I = (P/20)2
­ the ratio of the intensities of sound: I1/I2 = (P1/P2)2
A C O U S T I C S of W O O D
Lecture 1
1. About Amplitude ­ DECIBELS ­ the wide amplitude range of sound is often referred to in decibels; sound Pressure Level (dB SPL), relative to 0.0002 microbar (0dB SPL)
­ why?
­ Fechner (1860): the sensitivity of the ear to changes in intensity was not related linearly to either intensity or pressure, the ear's sensitivity to sound intensity or sound pressure was an approximately logarithmic relationship
­ it was proposed that a new measure of intensity be utilised which was derived from the log (base 10) of the ratio of two intensities:
Bel (IL) = log10 (I1 / I2)
­ this Bel scale (after Alexander Graham Bell) was approximately linearly related to the ear's sensitivity to sound intensity so that equal steps in Bels were close to equal perceptual steps. ­ step of 1 Bel was however about 10 times greater than the minimally perceivable step >>> so a new scale was devised, the deciBel (dB) .... 1 Bel = 10 dB
A C O U S T I C S of W O O D
Lecture 1
1. About Amplitude ­ DECIBELS So that:
dB = 10 x log10 (I1/I2)
­ 0dB SPL is the threshold of hearing and 120dB SPL is the threshold of pain; 1dB is about the smallest change in SPL that can be heard; A 3dB change is generally noticeable and a 6dB change is very noticeable
­ 6dB rise implies a doubling of sound pressure; 3dB rise implies a doubling of intensity; 6dB fall implies a halving of sound pressure; a 3dB fall implies a halving of sound intensity
­ there are slight differences in the reference levels which could result in significant differences in the resultant dB value for very low test intensities and pressures
dB (IL)
=
dB (IL: ref=10­12W.m­2)
10 x log(I/I0)
=
10 x log(I/I0)
dB (ref=10­12W.m­2)
=
10 x log(I/I0)
dB (SPL)
=
20 x log(P/P0)
dB (SPL: ref=20µPa)
=
20 x log(P/P0)
dB (ref=20µPa)
=
20 x log(P/P0)
­ the symbol dB without one of the qualifiers could imply that any pressure or intensity has been used as the reference
A C O U S T I C S of W O O D
Lecture 1
DECIBELS CALCULATIONS
­ all calculations should be carried out on sound intensities, never on sound pressures or dB values
­ to add together two sounds with known dB values and to determine the resultant amplitude in dB: convert both dB values to intensity I = 10(dB/10); add together the derived intensity values I = I1 + I2; convert the intensity back to dB = 10 x log10(I)
­ to add two sounds of the same dB value, simply add 3 dB
­ to double intensity, simply add 3 dB
­ to halve intensity, simply subtract 3 dB
­ multiplying intensity by four is the same as doubling twice, so add 3 dB twice
­ dividing intensity by four is the same as halving twice, so subtract 3 dB twice
­ when adding together two sounds the resultant dB value is somewhere between the higher original dB value and 3dB above that value ­­­ for two sounds of dB1 and dB2 (where the higher value is dB1) the resultant value is between dB1 and dB1+3 (the new value is only equal to dB1+3 when dB2 exactly equals dB1)
50 dB + 50 dB = 53 dB
50 dB + 47 dB = 51.8 dB
50 dB + 40 dB = 50.4 dB
50 dB + 20 dB = 50.004 dB
50 dB + 0 dB = 50.00004 dB (0 dB is not I = 0 !!!)
A C O U S T I C S of W O O D
Lecture 1
RMS ­ Root Mean Squared Average of Sound Pressure
­ this method is the only valid way to determine the "average" sound pressure of a length of sound
­ this is because pressures cannot be added together in a straightforward way but must be first converted to intensities
I = P2
­ the following formula can be used for the calculation of average pressure:
R.M.S. value is the SQUARE ROOT OF (THE AVERAGE OF (THE SUM OF (THE SQUARES OF (THE ORIGINAL PRESSURE VALUES)))).
A C O U S T I C S of W O O D
Lecture 1
... Amplitude
­ because the instantaneous value of the pressure in a sound wave changes rapidly with time, the amplitude is usually characterized by the root­mean­square, or rms, value of the pressure, a value based on time averaging.
­ the energy, or power, in a sound wave is proportional to the square of the pressure amplitude and is thus proportional to the meansquare value of pressure
­ in order to express the wide range of sound pressure amplitudes in a convenient form, a logarithmic metric has been universally adopted ­ this metric is the decibel, which expresses the level of a given sound in terms of the ratio (on a logarithmic basis) of the meansquare pressure of the sound to a reference meansquare pressure
­ word Amplitude generically reffer to the concept that includes Power, Intensity and Pressure. The terms "power" and "intensity" are used interchangeably by many authors...
­ what is measured directly at a microphone diaphragm is pressure or sound pressure level (SPL) which is a measure of the slight fluctuations in the ambient pressure of the medium. Once you have derived a pressure value you can then mathematically convert that into an intensity value.
A C O U S T I C S of W O O D
Lecture 1
­ the acoustic intensity diminishes with distance in accordance with the inverse square law:
I = 1 / r2
where: I is the intensity of a sound, r is the distance from the source of the sound
For comparing intensities (and pressures) at varying distances from the sound source use: distance [m] 1
2
4
32
vs. level [dB]
0
­ 6
­12
­30
A C O U S T I C S of W O O D
Lecture 1
About Frequency
­ the frequency of a sound wave is expressed in hertz (Hz), where one hertz is equal to one cycle per second
f=1/T
;
lambda=c/f=c.T ;
omega=2*PI*f
­ the range of frequencies that give rise to the sensation of pitch in humans extends roughly from 16 (20) Hz to 20,000 Hz, with much individual variation
­ sounds are not composed of only a single frequency ­ are instead a combination of many frequencies ­ the distribution of acoustical energy as a function of frequency is generally referred to as a spectrum. ­ the spectrum of the sound from a modern orchestra, for instance, will show energy concentrated from about 25 Hz to 5,000 Hz; the noise in a large computer room, from 30 Hz to 10,000 Hz
­ human listener perceives the spectrum of a sound as its quality or timbre (a violin playing middleC and a trumpet playing middleC have different qualities because their spectra are different)
A C O U S T I C S of W O O D
Lecture 1
About Frequency, Wavelength, Period, Speed of Sound
The wavelength (λ) of a wave is the distance between successive wave fronts (ie. peak­to­peak distance). Wavelength is measured in metres (m).
The frequency (f) of a wave is the number of times per second that a complete wave cycle passes an observer. Frequency is measured in Hertz (Hz).
The period (T) of a wave is the time it takes for one wave cycle to pass an observer. The period is measured in seconds (s) (in speech milliseconds (ms) are commonly used)
The speed or velocity of sound (c) is the number of metres that a wave front can travel in a second. The speed of sound is measured in metres/second (m.s­1)
A C O U S T I C S of W O O D
Lecture 1
About Frequency, Wawelenght and Speed
­ the distance between the sound compressions and rarefactions is known as wavelength. Low frequency sounds have a long wavelength and are perceived as low­pitched sounds such as the rumble of a truck. ­ high­pitched sounds have very short wavelengths such as sound emitted from a whistle. In the field of music a piano can generate sounds ranging from 20 cycles per second (Hz) all the way up to 4600 cycles per second.
­ relationships between period and frequency:
­ it is possible to calculate the frequency of a wave if you know its wavelength and the speed of sound. Conversely, you can calculate the wavelength of a wave from its frequency and the speed of sound. (Similarly, for period (T)).
A C O U S T I C S of W O O D
Lecture 1
About Frequency, Wawelenght and Speed – DOPPLERS EFFECT
­ when a sound source and an observer are stationary, the frequency observed by can be readily determined from the wavelength of the sound emitted by and the speed of sound according to the following formula:
f =c/ 
­ when an observer is moving towards a sound source, observer's ear intersects with each cycle peak more rapidly than would be predicted from the wavelength and the speed of sound
­ this has the same effect as would an increase in the speed of sound (increase in the observed frequency of the sound). ­ in these cases the effective speed of sound can be determined by adding v to c
f =cv/
A C O U S T I C S of W O O D
Lecture 1
Sound Velocity, Speed of Sound
­ varies from one medium to another:
Water
Rubber
Granite
Aluminium
Iron
Copper
Lead
Wood – parallel
Wood – perpendicular
15
0
0
20
20
20
20
20
20
1.0
1.1
2.7
2.7
7.9
8.9
11.3
0.5
0.5
1450
54
6000
5100
5130
3560
1230
cca 4000
cca 1500
­ at normal (1 atm.) pressure and 0°C the speed of sound in air is 331 m/s (1 km in 3 seconds)
A C O U S T I C S of W O O D
Lecture 1
Sound Velocity, Speed of Sound
­ the speed of sound is proportional to the temperature and inversely proportional to the density of the gas
 t   1/ 
­ effect of temperature change on the speed of sound within common temperature ranges (­50°C to +45°C) only results in moderate changes in the speed of sound
­ change in the speed of sound resulting from changes in temperature can be derived from the following formula:
c 2=c 1  t 1 / t 2
where: c1 and t1 are the speed of sound in and temperature (°K) of condition 1, c2 and t2 are the speed of sound in and temperature (°K) of condition 2
­ at ­50°C is 84% of c at +45°C >>> which would result in perceivable differences in the frequency of the same sound; speed of sound in Heliox mixtures is around twice the speed of sound in normal air >>> the fundamental frequency (pitch) and resonant peak (formant) frequencies are shifted to much higher
A C O U S T I C S of W O O D
Lecture 1
Sound Velocity, Speed of Sound
­ the speed of sound in a gas is dependent on a number of factors:
­ the composition of the gas (eg. air 80% oxygen + 20% nitrogen)
­ pressure
­ temperature
c=  g.p /
where: c is velocity of sound, p static pressure, rho static density and g is ratio of specific heats (it varies with gas and is proportional to temperature)
­ under conditions where pressure and density remain constant (eg. same gas under same pressure conditions, such as air at sea level) relation holds:
c2 =c1  t 1 / t 2
­ at 298°K (25°C) c = 346 m/s; 303°K (30°C) then c = 349 m/s; 273°K (0°C) then c = 331 m/s
A C O U S T I C S of W O O D
Lecture 1
Sound Velocity, Speed of Sound
­ velocity of sound in very low density gasses (hydrogen) tends to be higher than it is in higher density gasses
Water
Iron
Wood – radial
Hydrogen
Oxygen
Air
1.0
7.9
0.5
0.09
1.4
1.3
1450
5130
cca 1500
1286
317
331
­ the velocity of sound in liquids and solids depends upon the elasticity (k = elastic or bulk modulus) and density
c= k / 
­ elastic modulus increases as the compressibility or deformability of the material decreases, so the increases in either elasticity (decrease in k) or in density lead to a decrease in the speed of sound (see also different velocities in different mateials – caused by density but by the elasticity of material too)
A C O U S T I C S of W O O D
Lecture 1
Acoustic units ­ Owerview
name
abbreviation
basic u.
non­basic u.
Wavelength (λ):
metre
m
m Frequency (f):
Hertz
kiloHertz Hz
kHz
s­1
(cycles.s­1) (1000.s­1)
Period (T):
second
millisecond
s ms
s (10­3.s)
Speed of sound (c):
metre/sec
m/s
m.s­1 Acoustic Power (Pwr):
Watt
W
kg.m2.s­3 Acoustic Intensity (I):
Watt/sq.m.
W/m2
kg.s­3 (Joule.s­1.m­2)
Sound Pressure
(P, SPL):
Pascal microPascal
Pa µPa
kg.m­1.s­2
(Joule.s­1)
(Newton.m­2)
A C O U S T I C S of W O O D
Lecture 1
Ear and sound
­ sound enters the human ear canal of the outer ear and causes the eardrum to vibrate in response; these vibrations are coupled through three tiny bones in the middle ear to the main sensory organ in the inner ear, or cochlea
­ hair cells in the cochlea transmit nerve impulses along the auditory nerve to the brain, where they are interpreted as sound
­ the human ear does not respond to the pressure and frequency of a sound wave in the same way that an electronic measuring instrument does. A sound level meter might indicate the sound pressure level of a 60Hz tone to be 50 dB and the level of a 1000Hz tone to be 25 dB, yet to a listener the tones would be perceived as equally loud
­ this is because the sensitivity of the ear is not uniform (varies with frequency and level too) ­ at low sound pressure levels, we tend to hear midfrequencies better than higher frequencies, and much better than lower frequencies; at high sound pressure levels, the variation is not as pronounced and we tend to hear low, mid, and high frequencies about the same (we "lose the bass" when the volume is turned down low.)