plane and spherical waves, intensity

what is a plane wave?

in a plane wave, each wavefront (surface of equal phase) is infinite plane normal to direction of wave propagation

• no geometric attenuation

• no pure plane waves exist in reality

• sound fields act as plane waves far from source

practical plane and cylindrical wave approximations?

can be obtained with linear array constructions

• typically used at large outdoor concerts

• lower attenuation of sound as function of distance (compared to spherical waves)

what is a complex pressure wave?

plane wave propagating in positive x-direction can be given using complex representation

(take screenshot from slide 5/35 for formula and parameters explained)

note - exponents are purely imaginary → no losses

what is the wave number? 

k = 2π/λ = ω/c

corresponds to spatial freq

• the higher the k, the more vibrations per meter

kx = 2πx/λ

characteristic impedance of a plane wave?

(take ss of slide 6/35 for function and parameters)

solved example of finding particle velocity

ss of slide 7/35

what is energy density?

(acoustic) energy in unit volume

(ss formula frm 9/35)

• consists of kinetic (D_k) and potential (D_p) energy densities

• for plane waves

• (ss the rest)

what is the intensity vector I?

I denotes net power transmitted through unit area

can be derived from energy density:

• intensity obtained by multiplying energy density with energy propagation velocity 

• for plane waves, energy propagates at speed c

• | I | = (screenshot)

• generally for 3D vectors = I = pu

how can intensity of plane wave be estimated?

can be estimated if 2 of the following quantities are known:

• pressure p

• particle velocity u

• characteristic impedance z_c

any similarities with electric domain?

acoustic domain

• p = z_cu

• I = pu

electric domain

• U=ZI

• P=UI

what is acoustic intensity in general?

intensity denotes change of energy (power) through a surface

• obtained by multiplying pressure (scalar) and particle velocity (vector)

generally intensity is complex

can be divided into real and imaginary parts

THIS CARD IS NOT DONE

what holds for harmonic fields?

(basically ss the entire slide 13/35)

where can acoustic intensity be used?

identifying noise sources

measuring acoustic power

• Gauss law as applied to acoustics

what are spherical coordinates?

a point P can be given in spherical coordinates using

• radius r

• angle theta (from z-axis)

• angle fi (from x-axis)

relation to cartesian coordinates: (ss from slide 20)

what aboutcalculations

(slide 21)

what is acoustic center?

center of spherical sound waves radiating outward a sound source

what is 1/r law?

illustrates behaviour of sound field with relation to distance from source

• in effect, pressure

NOT DONE

what is 1/r² law?

illustrates behaviour of power with relation to distance from source

NOT DONE

what is charactersitic impedance of spherical wave?

can be derived from wave equation

(ss from slide 23)

what is near field?

relation between p and u differs from plane-wave case

• close to sound

NOT DONE

what is an elementary monopole?

consider sphere with radius R. the sphere pulsates, ie periodically increases and decreases its radius so that

• radial displacement is (copy character from slides)

• movement is sinusoidal, so radial velocity is

• freq of pulsation

NOT DONE

what is volume velocity (or source strength)?

it is created by the pulsating sphere

(ss equation from slide 27)

what is pressure wave at a distance r? 

(ss equation from slide 27)

what is the intensity created by elementary monopole?

active intensity in radiation direction (ss from slide 28)

acoustic power can be computed

what is mechanical radiation impedance?

MRI of a surface gives ratio between radial velocity and resulting force exerted on the surface by the fluid

• property of the vibrating surface and liquid

• not a property of the actual vibrating object

radiation impedance of a pulsating sphere is: (ss from slide 29)

what is attached mass?

girl just look at slide 30 i have no idea

we still have 5 slides left but we didnt get to that

upsiiiiii