acoustic work
TRANSCRIPT
-
7/28/2019 Acoustic Work
1/18
TERM PAPER
OF
WAVE ELECTRICITY & MAGNETISM
TOPIC:ACOUSTIC
SUBMITTED TO- SUBMITTED BY-
MR.NIRAJ KUMAR ANKIT SINGH
REG-NO.-10901672
ROLL-NO.-A34
SECTION:-M4901
-
7/28/2019 Acoustic Work
2/18
ACKNOWLEDGEMENT
History of all great works is to witness that nogreat work has ever done with others. The active or
passive support of a person surrounding and one
close quarter. Thus it is not hard to conclude how
active assistance from senior could positively
impact the execution of my term paper project. I
am highly thankful to specially PHYSICS teacher
NIRAJ KUMAR for the active guidance throughout
the completion of project.
ANKIT SINGH
LIT PHAGWARA
-
7/28/2019 Acoustic Work
3/18
Contents:-
Introduction
Acoustic music
Musical acoustics
Acoustic guitar
Acoustic impedance
Acoustic wave equation
Derivation
Reference
-
7/28/2019 Acoustic Work
4/18
Introduction:-
Acoustics, a branch of physics that studies sound, musical acoustics, the branch of
acoustics that studies the physics of music. External acoustic meatus, another name
for the ear canal. Acoustic recording, a pre-microphone method of recording used,
for instance, on the Graphophone
In music:
Acoustic music, music that solely or primarily uses acoustic instruments
An instrument used in acoustic music (see link above), such as:
Acoustic guitar, as opposed to electric guitar
Acoustic bass guitar, as opposed to electric bass guitar
Acoustic was released in 1995, and is the second live album to be released by the
group Deine Lakaien.
This live album was recorded during the sold-out 1995 Acoustic Tour. The songs
were performed unplugged, with Alexander Veljanov's vocals backed by Ernst
Horn on aprepared piano.
http://en.wikipedia.org/wiki/Acousticshttp://en.wikipedia.org/wiki/Musical_acousticshttp://en.wikipedia.org/wiki/External_acoustic_meatushttp://en.wikipedia.org/wiki/Graphophonehttp://en.wikipedia.org/wiki/Acoustic_musichttp://en.wikipedia.org/wiki/Acoustic_guitarhttp://en.wikipedia.org/wiki/Acoustic_bass_guitarhttp://en.wikipedia.org/wiki/Deine_Lakaienhttp://en.wikipedia.org/wiki/Acoustic_musichttp://en.wikipedia.org/wiki/Alexander_Veljanovhttp://en.wikipedia.org/wiki/Ernst_Hornhttp://en.wikipedia.org/wiki/Ernst_Hornhttp://en.wikipedia.org/wiki/Prepared_pianohttp://en.wikipedia.org/wiki/Musical_acousticshttp://en.wikipedia.org/wiki/External_acoustic_meatushttp://en.wikipedia.org/wiki/Graphophonehttp://en.wikipedia.org/wiki/Acoustic_musichttp://en.wikipedia.org/wiki/Acoustic_guitarhttp://en.wikipedia.org/wiki/Acoustic_bass_guitarhttp://en.wikipedia.org/wiki/Deine_Lakaienhttp://en.wikipedia.org/wiki/Acoustic_musichttp://en.wikipedia.org/wiki/Alexander_Veljanovhttp://en.wikipedia.org/wiki/Ernst_Hornhttp://en.wikipedia.org/wiki/Ernst_Hornhttp://en.wikipedia.org/wiki/Prepared_pianohttp://en.wikipedia.org/wiki/Acoustics -
7/28/2019 Acoustic Work
5/18
Acoustic music
An acoustic guitar
Acoustic music comprises music that is great or primarily uses instruments which
produce sound through entirely acoustic means, as opposed to electric orelectronic
means. The retronym "acoustic music" appeared after the advent of electric
instruments, such as the electric guitar,bass guitar, electric organ and synthesizer.
Performers of acoustic music often increase the volume of their output
using electronic amplifiers. However, these amplification devices remain
separate from the amplified instrument and reproduce its natural sound
accurately. Often a condenser microphone is placed in front of an acoustic
instument which is then wired up to an amp. This is the most effective way
of amplifying an acoustic instrument.
http://en.wikipedia.org/wiki/Acoustic_guitarhttp://en.wikipedia.org/wiki/Musichttp://en.wikipedia.org/wiki/Musical_instrumenthttp://en.wikipedia.org/wiki/Musical_acousticshttp://en.wikipedia.org/wiki/Electric_instrumenthttp://en.wikipedia.org/wiki/Electronic_musichttp://en.wikipedia.org/wiki/Retronymhttp://en.wikipedia.org/wiki/Electric_guitarhttp://en.wikipedia.org/wiki/Bass_guitarhttp://en.wikipedia.org/wiki/Electronic_organhttp://en.wikipedia.org/wiki/Synthesizerhttp://en.wikipedia.org/wiki/Electronic_amplifierhttp://en.wikipedia.org/wiki/File:Guitar_1.jpghttp://en.wikipedia.org/wiki/Acoustic_guitarhttp://en.wikipedia.org/wiki/Musichttp://en.wikipedia.org/wiki/Musical_instrumenthttp://en.wikipedia.org/wiki/Musical_acousticshttp://en.wikipedia.org/wiki/Electric_instrumenthttp://en.wikipedia.org/wiki/Electronic_musichttp://en.wikipedia.org/wiki/Retronymhttp://en.wikipedia.org/wiki/Electric_guitarhttp://en.wikipedia.org/wiki/Bass_guitarhttp://en.wikipedia.org/wiki/Electronic_organhttp://en.wikipedia.org/wiki/Synthesizerhttp://en.wikipedia.org/wiki/Electronic_amplifier -
7/28/2019 Acoustic Work
6/18
Following the increasing popularity of the television show MTV
Unplugged during the 1990s, acoustic (though in most cases stillelectrically-amplified) performances by musical artists who usually rely on
electronic instruments became colloquially referred to as "unplugged"
performances.
Writing forSplendid, music reviewer Craig Conley suggests, "When music
is labeled acoustic, unplugged, or unwired, the assumption seems to be that
other types of music are cluttered by technology and overproduction and
therefore aren't as pure."[2]
Musical acoustics
Musical acoustics or music acoustics is the branch of acoustics concerned with
researching and describing thephysics ofmusic how sounds employed as music
work. Examples of areas of study are the function of musical instruments, the
human voice (the physics of speech and singing), computer analysis of melody,
and in the clinical use of music in music therapy.
Harmonics, partials, and overtones
http://en.wikipedia.org/wiki/Television_showhttp://en.wikipedia.org/wiki/MTV_Unpluggedhttp://en.wikipedia.org/wiki/MTV_Unpluggedhttp://en.wikipedia.org/wiki/1990shttp://en.wikipedia.org/wiki/Musicianhttp://en.wikipedia.org/wiki/Splendidhttp://en.wikipedia.org/wiki/Audio_technologyhttp://en.wikipedia.org/wiki/Overproduction_(music)http://en.wikipedia.org/wiki/Acoustic_music#cite_note-1http://en.wikipedia.org/wiki/Acousticshttp://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Musichttp://en.wikipedia.org/wiki/Musical_instrumentshttp://en.wikipedia.org/wiki/Human_voicehttp://en.wikipedia.org/wiki/Interpersonal_communicationhttp://en.wikipedia.org/wiki/Singinghttp://en.wikipedia.org/wiki/Melodyhttp://en.wikipedia.org/wiki/Music_therapyhttp://en.wikipedia.org/wiki/File:Moodswingerscale.jpghttp://en.wikipedia.org/wiki/Television_showhttp://en.wikipedia.org/wiki/MTV_Unpluggedhttp://en.wikipedia.org/wiki/MTV_Unpluggedhttp://en.wikipedia.org/wiki/1990shttp://en.wikipedia.org/wiki/Musicianhttp://en.wikipedia.org/wiki/Splendidhttp://en.wikipedia.org/wiki/Audio_technologyhttp://en.wikipedia.org/wiki/Overproduction_(music)http://en.wikipedia.org/wiki/Acoustic_music#cite_note-1http://en.wikipedia.org/wiki/Acousticshttp://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Musichttp://en.wikipedia.org/wiki/Musical_instrumentshttp://en.wikipedia.org/wiki/Human_voicehttp://en.wikipedia.org/wiki/Interpersonal_communicationhttp://en.wikipedia.org/wiki/Singinghttp://en.wikipedia.org/wiki/Melodyhttp://en.wikipedia.org/wiki/Music_therapy -
7/28/2019 Acoustic Work
7/18
Scale of harmonics
The fundamental is the frequency at which the entire wave vibrates. Overtones are
other sinusoidal components present at frequencies above the fundamental. All of
the frequency components that make up the total waveform, including thefundamental and the overtones, are called partials. Together they form the
harmonic series.
Overtones which are perfect integer multiples of the fundamental are called
harmonics. When an overtone is near to being harmonic, but not exact, it is
sometimes called a harmonic partial, although they are often referred to simply as
harmonics. Sometimes overtones are created that are not anywhere near a
harmonic, and are just called partials or inharmonic overtones.
The fundamental frequency is considered the first harmonic and the first partial.The numbering of the partials and harmonics is then usually the same; the second
partial is the second harmonic, etc. But if there are inharmonic partials, the
numbering no longer coincides. Overtones are numbered as they appear above the
fundamental. So strictly speaking, the first overtone is the second partial (and
usually the second harmonic). As this can result in confusion, only harmonics are
usually referred to by their numbers, and overtones and partials are described by
their relationships to those harmonics.
Harmonics and non-linearities
A half-wave symmetric and asymmetric waveform. The red contains only the
fundamental and odd harmonics, the green contains the fundamental, odd, and
even harmonics.
http://en.wikipedia.org/wiki/Scale_of_harmonicshttp://en.wikipedia.org/wiki/Partialhttp://en.wikipedia.org/wiki/Harmonic_series_(music)http://en.wikipedia.org/wiki/Harmonichttp://en.wikipedia.org/wiki/File:Symmetricandasymmetricwaveforms.pnghttp://en.wikipedia.org/wiki/Scale_of_harmonicshttp://en.wikipedia.org/wiki/Partialhttp://en.wikipedia.org/wiki/Harmonic_series_(music)http://en.wikipedia.org/wiki/Harmonic -
7/28/2019 Acoustic Work
8/18
200 and 300 Hz waves and their sum, showing the periods of each.
A spectrogram of a violin playing a note and then a perfect fifth above it. The
shared partials are highlighted by the white dashes.
When a periodic wave is composed of a fundamental and only odd harmonics (f,
3f, 5f, 7f, ...), the summed wave is half-wave .
http://en.wikipedia.org/wiki/File:Spectrogram_showing_shared_partials.pnghttp://en.wikipedia.org/wiki/File:Perfect_fifth_graphs.png -
7/28/2019 Acoustic Work
9/18
Harmony
If two notes are simultaneously played, with frequency ratios that are simple
fractions (e.g. 2/1, 3/2 or 5/4), then the composite wave will still be periodic with a
short period, and the combination will sound consonant. For instance, a notevibrating at 200 Hz and a note vibrating at 300 Hz (a perfect fifth, or 3/2 ratio,
above 200 Hz) will add together to make a wave that repeats at 100 Hz: every
1/100 of a second, the 300 Hz wave will repeat thrice and the 200 Hz wave will
repeat twice. Note that the total wave repeats at 100 Hz, but there is not actually a
100 Hz sinusoidal component present.
Additionally, the two notes will have many of the same partials. For instance, a
note with a fundamental frequency of 200 Hz will have harmonics at:
(200,) 400, 600, 800, 1000, 1200,
A note with fundamental frequency of 300 Hz will have harmonics at:
(300,) 600, 900, 1200, 1500,
The two notes have the harmonics 600 and 1200 in common, and more will
coincide further up the series.
The combination of composite waves with short fundamental frequencies andshared or closely related partials is what causes the sensation ofharmony.
When two frequencies are near to a simple fraction, but not exact, the composite
wave cycles slowly enough to hear the cancellation of the waves as a steady
pulsing instead of a tone. This is calledbeating, and is considered to be unpleasant,
ordissonant.
The frequency of beating is calculated as the difference between the frequencies of
the two notes. For the example above, |200 Hz - 300 Hz| = 100 Hz. As another
example, a combination of 3425 Hz and 3426 Hz would beat once per second (|3425 Hz - 3426 Hz| = 1 Hz). This follows from modulation theory.
http://en.wikipedia.org/wiki/Ratiohttp://en.wikipedia.org/wiki/Consonancehttp://en.wikipedia.org/wiki/Perfect_fifthhttp://en.wikipedia.org/wiki/Harmonyhttp://en.wikipedia.org/wiki/Beat_(acoustics)http://en.wikipedia.org/wiki/Consonance_and_dissonancehttp://en.wikipedia.org/wiki/Modulationhttp://en.wikipedia.org/wiki/Ratiohttp://en.wikipedia.org/wiki/Consonancehttp://en.wikipedia.org/wiki/Perfect_fifthhttp://en.wikipedia.org/wiki/Harmonyhttp://en.wikipedia.org/wiki/Beat_(acoustics)http://en.wikipedia.org/wiki/Consonance_and_dissonancehttp://en.wikipedia.org/wiki/Modulation -
7/28/2019 Acoustic Work
10/18
Acoustic guitar
A modern acoustic guitar.
An acoustic guitar is a guitarthat uses only acoustic methods to project the sound
produced by its strings. The term is a retronym, coined after the advent ofelectric
guitars, which rely on electronic amplification to make their sound audible.
Types
Historical and modern acoustic guitars are extremely varied in their design and
construction, far more so than electric guitars. Some of the most important
varieties are the classical guitar (nylon-stringed), steel-string acoustic guitar and
lap steel guitar. A more complete list is given below, refer to the individual articles
for more specific detail.
Nylon/gut stringed guitars:
o Renaissance guitar
o Baroque guitar
o Romantic guitar
o Classical guitar, the modern version of the original guitar, with nylon
strings
o Flamenco guitar
http://en.wikipedia.org/wiki/Guitarhttp://en.wikipedia.org/wiki/Retronymhttp://en.wikipedia.org/wiki/Electric_guitarhttp://en.wikipedia.org/wiki/Electric_guitarhttp://en.wikipedia.org/wiki/Classical_guitarhttp://en.wikipedia.org/wiki/Steel-string_acoustic_guitarhttp://en.wikipedia.org/wiki/Lap_steel_guitarhttp://en.wikipedia.org/wiki/Baroque_guitarhttp://en.wikipedia.org/wiki/Romantic_guitarhttp://en.wikipedia.org/wiki/Classical_guitarhttp://en.wikipedia.org/wiki/Flamenco_guitarhttp://en.wikipedia.org/wiki/File:AcousticGuitar.jpghttp://en.wikipedia.org/wiki/Guitarhttp://en.wikipedia.org/wiki/Retronymhttp://en.wikipedia.org/wiki/Electric_guitarhttp://en.wikipedia.org/wiki/Electric_guitarhttp://en.wikipedia.org/wiki/Classical_guitarhttp://en.wikipedia.org/wiki/Steel-string_acoustic_guitarhttp://en.wikipedia.org/wiki/Lap_steel_guitarhttp://en.wikipedia.org/wiki/Baroque_guitarhttp://en.wikipedia.org/wiki/Romantic_guitarhttp://en.wikipedia.org/wiki/Classical_guitarhttp://en.wikipedia.org/wiki/Flamenco_guitar -
7/28/2019 Acoustic Work
11/18
o Extended-range classical guitar
A steel strung Yamaha APX700 electric-acoustic guitar
Acoustic impedance
The acoustic impedance Z (or sound impedance) is a frequency (f) dependentparameter is very useful, for example, for describing the behaviour of musical
wind instruments. Mathematically, it is the sound pressure p divided by theparticle
velocity v and the surface area S, through which an acoustic wave of frequency f
propagates. If the impedance is calculated for a range of excitation frequencies
the result is an impedance curve. Plane, single-frequency traveling waves have
acoustic impedance equal to the characteristic impedance divided by the surface
area, where the characteristic impedance is the product of longitudinal wave
velocity and density of the medium. Acoustic impedance can be expressed in either
its constituent units (pressure per velocity per area) or in rayls.
Note that sometimes vS is referred to as the volume velocity.
http://en.wikipedia.org/wiki/Extended-range_classical_guitarhttp://en.wikipedia.org/wiki/Sound_pressurehttp://en.wikipedia.org/wiki/Particle_velocityhttp://en.wikipedia.org/wiki/Particle_velocityhttp://en.wikipedia.org/wiki/Traveling_wavehttp://en.wikipedia.org/wiki/Longitudinal_wavehttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Raylhttp://en.wikipedia.org/wiki/File:Yamahaapx700.jpghttp://en.wikipedia.org/wiki/Extended-range_classical_guitarhttp://en.wikipedia.org/wiki/Sound_pressurehttp://en.wikipedia.org/wiki/Particle_velocityhttp://en.wikipedia.org/wiki/Particle_velocityhttp://en.wikipedia.org/wiki/Traveling_wavehttp://en.wikipedia.org/wiki/Longitudinal_wavehttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Rayl -
7/28/2019 Acoustic Work
12/18
The specific acoustic impedance z is the ratio of sound pressure p to particle
velocity v at a single frequency. Therefore
Distinction has to be made between:
the characteristic acoustic impedance Z0 of a medium, usually air (compare
with characteristic impedance in transmission lines).
the impedance Z of an acoustic component, like a wave conductor, a
resonance chamber, a muffler or an organ pipe.
Acoustic wave equation
Inphysics, the acoustic wave equation governs the propagation of acoustic waves
through a material medium. The form of the equation is a second orderpartial
differential equation. The equation describes the evolution ofacoustic pressure p or
particle velocity as a function of position and time t. A simplified form of the
equation describes acoustic waves in only one spatial dimension (position x), whilea more general form describes waves in three dimensions (displacement vector
).
In one dimension
Equation
where p is the acoustic pressure (the local deviation from the ambient pressure),
and where c is the speed of sound.
http://en.wikipedia.org/wiki/Sound_pressurehttp://en.wikipedia.org/wiki/Particle_velocityhttp://en.wikipedia.org/wiki/Particle_velocityhttp://en.wikipedia.org/wiki/Characteristic_impedancehttp://en.wikipedia.org/wiki/Transmission_linehttp://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Partial_differential_equationhttp://en.wikipedia.org/wiki/Partial_differential_equationhttp://en.wikipedia.org/wiki/Acoustic_pressurehttp://en.wikipedia.org/wiki/Particle_velocityhttp://en.wikipedia.org/wiki/Acoustic_pressurehttp://en.wikipedia.org/wiki/Speed_of_soundhttp://en.wikipedia.org/wiki/Sound_pressurehttp://en.wikipedia.org/wiki/Particle_velocityhttp://en.wikipedia.org/wiki/Particle_velocityhttp://en.wikipedia.org/wiki/Characteristic_impedancehttp://en.wikipedia.org/wiki/Transmission_linehttp://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Partial_differential_equationhttp://en.wikipedia.org/wiki/Partial_differential_equationhttp://en.wikipedia.org/wiki/Acoustic_pressurehttp://en.wikipedia.org/wiki/Particle_velocityhttp://en.wikipedia.org/wiki/Acoustic_pressurehttp://en.wikipedia.org/wiki/Speed_of_sound -
7/28/2019 Acoustic Work
13/18
Solution
Provided that the speed c is a constant, not dependent on frequency (the
dispersionless case), then the most general solution is
p = f(ct x) + g(ct + x)
where f and g are any two twice-differentiable functions. This may be pictured as
the superposition of two waveforms of arbitrary profile, one (f) travelling up the x-
axis and the other (g) down the x-axis at the speed c. The particular case of a
sinusoidal wave travelling in one direction is obtained by choosing either f or g to
be a sinusoid, and the other to be zero, giving
.
where is the angular frequency of the wave and k is its wave number.
Derivation
The wave equation can be developed from the linearized one-dimensional
continuity equation, the linearized one-dimensional force equation and the
equation of state.
The equation of state (ideal gas law)
PV = nRT
In an adiabatic process, pressure P as a function of density can be linearized to
where C is some constant. Breaking the pressure and density into their mean and
total components and noting that :
.
The adiabaticbulk modulus for a fluid is defined as
http://en.wikipedia.org/wiki/Superposition_principlehttp://en.wikipedia.org/wiki/Angular_frequencyhttp://en.wikipedia.org/wiki/Wave_numberhttp://en.wikipedia.org/wiki/Wave_numberhttp://en.wikipedia.org/wiki/Bulk_modulushttp://en.wikipedia.org/wiki/Superposition_principlehttp://en.wikipedia.org/wiki/Angular_frequencyhttp://en.wikipedia.org/wiki/Wave_numberhttp://en.wikipedia.org/wiki/Bulk_modulus -
7/28/2019 Acoustic Work
14/18
which gives the result
.
Condensation, s, is defined as the change in density for a given ambient fluid
density.
The linearized equation of state becomes
where p is the acoustic pressure(P P0).
The continuity equation (conservation of mass) in one dimension is
.
Again the equation must be linearized and the variables split into mean andvariable components.
Rearranging and noting that ambient density does not change with time or position
and that the condensation multiplied by the velocity is a very small number:
Euler's Force equation (conservation of momentum) is the last needed component.
In one dimension the equation is:
http://en.wikipedia.org/wiki/Continuity_equationhttp://en.wikipedia.org/wiki/Continuity_equation -
7/28/2019 Acoustic Work
15/18
,
where D / Dt represents the convective, substantial or material derivative, which is
the derivative at a point moving with medium rather than at a fixed point.
Linearizing the variables:
.
Rearranging and neglecting small terms, the resultant equation is:
.
Taking the time derivative of the continuity equation and the spatial derivative of
the force equation results in:
.
Multiplying the first by 0, subtracting the two, and substituting the linearized
equation of state,
.
The final result is
where is the speed of propagation.
http://en.wikipedia.org/wiki/Convective_derivativehttp://en.wikipedia.org/wiki/Convective_derivative -
7/28/2019 Acoustic Work
16/18
In three dimensions
Equation
where is the Laplace operator, p is the acoustic pressure (the local deviation
from the ambient pressure), and where c is the speed of sound.
Solution
The following solutions are obtained by separation of variables in different
coordinate systems. They are phasorsolutions, that is they have an implicit time-
dependence factor of eit where = 2f is the angular frequency. The explicit time
dependence is given by
Here is the wave number.
Cartesian coordinates
.
Cylindrical coordinates
.
where the asymptotic approximations to the Hankel functions, when , are
.
http://en.wikipedia.org/wiki/Laplace_operatorhttp://en.wikipedia.org/wiki/Acoustic_pressurehttp://en.wikipedia.org/wiki/Speed_of_soundhttp://en.wikipedia.org/wiki/Separation_of_variables#Partial_differential_equationshttp://en.wikipedia.org/wiki/Phasor_(sine_waves)http://en.wikipedia.org/wiki/Angular_frequencyhttp://en.wikipedia.org/wiki/Wave_numberhttp://en.wikipedia.org/wiki/Hankel_functionhttp://en.wikipedia.org/wiki/Laplace_operatorhttp://en.wikipedia.org/wiki/Acoustic_pressurehttp://en.wikipedia.org/wiki/Speed_of_soundhttp://en.wikipedia.org/wiki/Separation_of_variables#Partial_differential_equationshttp://en.wikipedia.org/wiki/Phasor_(sine_waves)http://en.wikipedia.org/wiki/Angular_frequencyhttp://en.wikipedia.org/wiki/Wave_numberhttp://en.wikipedia.org/wiki/Hankel_function -
7/28/2019 Acoustic Work
17/18
Spherical coordinates
.
Depending on the chosen Fourier convention, one of these represents on outwardtravelling wave and the other an unphysical inward travelling wave.
Reference
-
7/28/2019 Acoustic Work
18/18
www.google.in
www.wikkipedia.com
foundation of physics
http://www.google.in/http://www.wikkipedia.com/http://www.google.in/http://www.wikkipedia.com/