Acoustic Work

7/28/2019 Acoustic Work

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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


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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


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Contents:-

Introduction

Acoustic music

Musical acoustics

Acoustic guitar

Acoustic impedance

Acoustic wave equation

Derivation

Reference


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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,

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


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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


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Spherical coordinates

.

Depending on the chosen Fourier convention, one of these represents on outwardtravelling wave and the other an unphysical inward travelling wave.

Reference


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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/

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