CHAPTER IV RADIATION BY SIMPLE ACOUSTIC SOURCE. or by vibratory forces acting directly on the fluid, or by the violent motion of the fluid itself.

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1 CHAPTER IV RADIATION BY SIMPLE ACOUSTIC SOURCE 4.1 POINT SOURCE Sound waves ae geneated by the vibation of any solid body in contact with the fluid medium o by vibatoy foces acting diectly on the fluid, o by the violent motion of the fluid itself. In each case enegy is tansfeed fom the souce to the fluid. The chaacteistics of the souce geneated sound field; ecipocally, the diectional popeties of the field can be used to shed light on the natue of the souce. Any motion of one potion of the fluid medium is tansmitted to othe pats of the medium; the motion in the fontal egion of a sound wave at one instant may be egaded as the souce of the subsequent wave motion, fathe along in the medium. But in this case the enegy of the wave is just being tansmitted fom one pat to anothe; no new enegy being intoduced. In this cases mentioned in the fist paagaph, howeve, enegy oiginally not acoustic is being changed to acoustic enegy at the souce, to be adiated outwad and lost to the souce. Fom a point of view of acoustics, a souce is a egion in space, in contact with the fluid medium, whee new acoustic enegy is being geneated, to be adiated outwad as sound waves. We shall devote ou attention to the geneated sound waves as they move outwad fom the souce.to do so we shall assume that the fluid medium outside the souce egion is initially unifom and at est and that the acoustic pessue geneated outside the souce is small enough so that the fist ode equations of sound, deived in the peceding chapte ae valid in the egion outside the souce. In this chapte we will discuss the adiation of sound pessue by the simple acoustic souce, e.g monopole, dipole, quadupole etc. 62

2 4.2 MONOPOLE A monopole is a souce which adiates sound equally well in all diections. The simplest example of a monopole souce would be a sphee whose adius altenately expands and contacts sinusoidally. The monopole souce ceates a sound wave by altenately intoducing and emoving fluid into the suounding aea. A boxed loudspeake at low fequencies acts as a as a monopole. The diectivity patten fo a monopole souce is shown in the figue at ight. The amplitude of pessue [Pa] at some distance [m] is given by p() Qk i c (4.1) 4 whee = density of wate [kgm -3 ], c = speed of sound [ms -1 ], = fequency [ads -1 ] (= 2 f ) f is the fequency in Hz,, t = time [s], k = wave numbe [m -1 ] and Q = souce stength [m 3 s -1 ]. The souce stength Q is the poduct of the suface aea and the nomal suface velocity of the monopole. While the density of the wate is 1000 kgm -3, speed of the sound c = 1500 ms -1, souce fequency f = 20 Hz and the souce stength be 1 m 3 s -1 then the sound adiation by the monopole will be shown by Fig 4.1a and Fig 4.1 b 63

Fig 4.1 a: Fixed distance at = 5 Fig 4.1 b: vaying distance fo = 1 to 10 4.

3 Fig 4.1 a: Fixed distance at = 5 Fig 4.1 b: vaying distance fo = 1 to DIPOLE A dipole souce consists of two monopole souces of equal stength but opposite phase and sepaated by a small distance compaed with the wavelength of sound. While one souce expands the othe souce contacts. The esult is that the fluid (ai) nea the two souces sloshes back and foth to poduce the sound. A sphee which oscillates back and foth acts like a dipole souce, as does an unboxed loudspeake (while the font is pushing outwads the back is sucking in). A dipole souce does not adiate sound in all diections equally. The diectivity patten shown at ight looks like a figue-8; thee ae two egions whee sound is adiated vey well, and two egions whee sound cancels. The amplitude of pessue [Pa] at some distance [m] is given by 64

4 2 Qk d p( ) i c cos( ) (4.2) 4 whee d = the hoizontal distance between two souces, = density of wate [kgm -3 ], c = speed of sound [ms -1 ], = fequency [ads -1 ] (= 2 f ) f is the fequency in Hz,, t = time [s], k = wave numbe [m -1 ] and Q = souce stength [m 3 s -1 ]. The souce stength Q is the poduct of the suface aea and the nomal suface velocity of the monopole. While the hoizontal distance between two souces d is m, the density of the wate is 1000 kgm -3, speed of the sound c = 1500 ms -1, souce fequency f = 20 Hz and the souce stength be 1 m 3 s -1 then the sound adiation by the monopole will be shown by Fig 4.2a and Fig 4.2 b. Fig 4.2 a: Fixed distance at = 5 Fig 4.2 b: vaying distance fo = 1 to 10 65

5 4.4 Quadupole This can be consideed as fou monopoles with two out of phase with the othe two. They ae eithe aanged in a line with altenating phase o at the vetices of a cube with opposite cones in phase. In the case of the quadupole, thee is no net flux of fluid and no net foce on the fluid. It is the fluctuating stess on the fluid that geneates the sound waves. Howeve, since fluids dont suppot shea stesses well, quadupoles ae poo adiatos of sound. The amplitude of pessue [Pa] at some distance [m] is given by 2 Qk p(, ) i c dd cos( )sin( ) (4.3) 4 whee d = the hoizontal distance, D = vetical distance between two souces, = density of wate [kgm -3 ], c = speed of sound [ms -1 ], = fequency [ads -1 ] (= 2 f ) f is the fequency in Hz,, t = time [s], k = wave numbe [m -1 ] and Q = souce stength [m 3 s -1 ]. The souce stength Q is the poduct of the suface aea and the nomal suface velocity of the monopole. While the hoizontal distance between two souces d is m, the vetical distance D is m, the density of the wate is 1000 kgm -3, speed of the sound c = 1500 ms -1, souce fequency f = 20 Hz and the souce stength be 1 m 3 s -1 then the sound adiation by the monopole will be shown by Fig 4.3a and Fig 4.3 b. 66

Fig 4.3 a: Fixed distance at = 5 Fig 4.3 b: vaying distance fo = 1 to 10 4.

The amplitude of pessue [Pa] at some distance [m] is given by Qk 2 2 p(, ) c 4k dd cos ( ) (4.

6 Fig 4.3 a: Fixed distance at = 5 Fig 4.3 b: vaying distance fo = 1 to Longitudinal Quadupole The quadupole aanged in a line with altenating phase is longitudinal quadupole. The amplitude of pessue [Pa] at some distance [m] is given by Qk 2 2 p(, ) c 4k dd cos ( ) (4.4) 4 whee d = the distance of two consecutive souces, D = distance between each pai of souces, = density of wate [kgm -3 ], c = speed of sound [ms -1 ], = fequency [ads -1 ] (= 2 f ) f is 67

7 the fequency in Hz,, t = time [s], k = wave numbe [m -1 ] and Q = souce stength [m 3 s -1 ]. The souce stength Q is the poduct of the suface aea and the nomal suface velocity of the monopole. While the hoizontal distance between two souces d is m, the vetical distance D is m, the density of the wate is 1000 kgm -3, speed of the sound c = 1500 ms -1, souce fequency f = 20 Hz and the souce stength be 1 m 3 s -1 then the sound adiation by the monopole will be shown by Fig 4.3a and Fig 4.3 b. Fig 4.4 a: Fixed distance at = 5 Fig 4.4 b: vaying distance fo = 1 to 10 The Eqs. 4.1 to 4.4 ae implemented to the MATLAB function Sound_Field_Radiated_By_ Simple_Souces_Calc and is given in the Table 4.1. Table 4.1: Sound_Field_Radiated_By_Simple_Souces_Calc %**************************************************************************** % Sound Field calculation %**************************************************************************** function []= Sound_Field_Radiated_By_Simple_Souces_Calc(distance) global density sound_speed fequency stength hdistance vdistance souce_type 68

8 ho = density; c = sound_speed; f = fequency; Q = stength; w = 2*pi*f; k = w/c; theta= 0:0.01:2*pi; % Souce Type : Monopole if souce_type == 1 figue() fo l= 1:1: length(distance) = distance(l); fo m= 1:1: length(theta) pessue(l,m)= abs(q*((i*k*ho*c)/(4*pi*))); pola(theta, pessue(l,:)) hold on hold off % Souce Type : Dipole if souce_type == 2 d = hdistance; figue() fo l= 1:1: length(distance) = distance(l); fo m= 1:1: length(theta) f_theta= theta(m); pessue(l,m)= abs(((-i*q*ho*c*(k^2)*d)/(4*pi*))*... cos(f_theta)); pola(theta, pessue(l,:)) hold on hold off % Souce Type : Quadupole if souce_type == 3 d= hdistance; D= vdistance; figue() fo l= 1:1: length(distance) = distance(l); fo m= 1:1: length(theta) f_theta= theta(m); pessue(l,m)= abs((q*ho*c*k)*(pi*)*(k^2*d)*d*... cos(f_theta)*sin(f_theta)); pola(theta, pessue(l,:)) hold on 69

9 hold off % Souce Type : Longitudial Quadupole if souce_type == 4 d= hdistance; D= vdistance; figue() fo l= 1:1: length(distance) = distance(l); fo m= 1:1: length(theta) f_theta= theta(m); pessue(l,m)= abs(((q*ho*c*k)/(pi*))*(k^2)*d*d*((cos(f_theta)^2))); pola(theta, pessue(l,:)) hold on hold off 70

Objects usually are charged up through the transfer of electrons from one object to the other.

Objects usually are charged up through the transfer of electrons from one object to the other. 1 Pat 1: Electic Foce 1.1: Review of Vectos Review you vectos! You should know how to convet fom pola fom to component fom and vice vesa add and subtact vectos multiply vectos by scalas Find the esultant