Applied Acoustics Applied Acoustics

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Applied Acoustics Applied Acoustics

http://pcfarina.eng.unipr.it/Acoustics-2012.htm http://pcfarina.eng.unipr.it/Acoustics-2012.htm

Angelo Farina

Dip. di Ingegneria Industriale - Università di Parma Parco Area delle Scienze 181/A, 43100 Parma – Italy

angelo.farina@unipr.it

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Lesson 01 Lesson 01

Basics of Sound

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SOUND

• Sound is generated by pressure variations in a medium (fluid or solid) that propagate without particle transport. But each particle moves back and forth around its equilibrium position with a certain particle velocity

• Is is characterized by

fundamental measurements such as Amplitude,

frequency or oscillation

period, wavelength and

propagation speed in the

medium.

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Basics of Sound: general properties Basics of Sound: general properties

Sound is characterized by the propagation of mechanical energy caused by a rapid succession of compressions and expansions in an elastic medium; this energy, which originates from a sound source, propagates through the medium in waves travelling with finite speed.

In order for sound to occur it is thus necessary to have:

• a “sound source”

• an “elastic medium”

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Sound source(1):

Simplest case: a plane surface having an harmonic motion at one end of an infinitely-long duct filled with an elastic medium at rest.

Compressions

Expansions

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Sound source(2):

The harmonic motion of the piston is characterized by the following quantities:

“f” = frequency, number of oscillations in a second, measured in

“Hertz” (Hz);

“T” = period, duration of a cycle, measured in seconds (s);

“” = angular velocity, measured in rad/s;

Relationships between the quantities:

f = 1/T and f = / 2 (Hz)

If the frequency is between 20 and 20000 Hz, the perturbation will be perceivable to the human ear, and it will be defined as sound or noise.

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Sound source (3):

The piston surface make a simple harmonic motion:

• displacement = s = s_o cos(t),

• velocity = v = ds/dt = -s_o sen ( t),

• acceleration = a = dv/dt = - ² s_o cos( t), where s_o is the value of maximum displacement.

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Elastic medium:

The elastic and mass properties of the elastic medium determine the

“speed” of transmission of the perturbation.

Wavelength

Sound speed c

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Sound speed and wavelenght:

The pressure perturbation propagates form the source in the medium, with a sound speed “c₀” which in dry air depends just from the centigrade temperature t, following the approximate relationships:

• c₀ = 331.4 + 0.6t (m/s)

the wavelenght “”, is related to the frequency of harmonic motion in the relationship:

•

 = c

⁰

f ( m)

c

₀

= g × R×T g =1.41

R= 287 ( J / kgK )

T = t+ 273 (K)

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Relationship between frequency and wavelenght:

When frequency increases, the wavelength becomes smaller and smaller…

Wavelenght

frequency

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Sound speed in different mediums:

• sound speed in water:

• sound speed in solids

• sound speed in air @ 20°C

 340 m/s

) / (

) / ( .

3 2

m kg density

m N m elastic E

c E

=

