applied acoustics angelo farina dip. di ingegneria industriale - università di parma parco area...

Applied AcousticsApplied Acousticshttp://pcfarina.eng.unipr.it/Acoustics-2012.htmhttp://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

5th October 2012 Basics of Sound 1

Lesson 01Lesson 01Basics of SoundBasics of Sound

5th October 2012 Basics of Sound 2

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.

5th October 2012 Basics of Sound 3

Basics of Sound: general propertiesBasics 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”

5th October 2012 Basics of Sound 4

Sound source(1):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

5th October 2012 Basics of Sound 5

Sound source(2):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.

5th October 2012 Basics of Sound 6

Sound source (3):Sound source (3):

The piston surface make a simple harmonic motion:

• displacement = s = so cos(t),

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

• acceleration = a = dv/dt = - 2 so cos( t),

where so is the value of maximum displacement.

5th October 2012 Basics of Sound 7

Elastic medium:Elastic medium:

The elastic and mass properties of the elastic medium determine the “speed” of transmission of the perturbation.

Wavelength

Sound speed c

5th October 2012 Basics of Sound 8

Sound speed and wavelenght: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:

•5th October 2012 Basics of Sound 9

Relationship between frequency and wavelenght:Relationship between frequency and wavelenght:

When frequency increases, the wavelength becomes smaller and smaller…

Wavelenght

frequency

5th October 2012 Basics of Sound 10

Sound speed in different mediums:Sound speed in different mediums:

• sound speed in water:

• sound speed in solids• sound speed in air @ 20°C

340 m/s

)/(

)/(.

3

2

mkgdensity

mNmelasticE

Ec

5th October 2012 Basics of Sound 11