sign in sign up
<<
Home , Particle velocity, Sound energy density, Sound intensity, Sound power

CHAPTER II

IMPORTANT ACOUSTIC QUANTITY

2.1 INVERSE SQUARE LAW

2.1.1 INTENSITY

The or acoustic intensity ( I ) is defined as the ( Pac ) per unit area ( A ). The usual context is the noise measurement of sound intensity in the air at a

listener's location. For instantaneous acoustic pressure ptinst ()and vt() the average acoustic intensity during time T is given by

1 T I p()() t v t dt . (2.1)  inst T 0

Notice that both and I are vectors, which means that both have a direction as well as a magnitude. The direction of the intensity is the average direction in which the energy is flowing. The SI units of intensity are W/m2 (watts per square meter).

For a spherical sound source, the intensity in the radial direction as a function of distance, r, from the centre of the source is as follows

PP I ac ac (2.2) r Ar4 2 where Pac is the sound power and A the surface area of a sphere of radius r. Thus the

1 sound intensity decreases with ,where r is the distance from an acoustic point source. r 2

1 I  (2.3) r 2

2 Ir12  2 (2.4) Ir21

25 2 r1 II21 2 (2.5) r2

2.1.2 SOUND INTENSITY LEVEL

Sound intensity level or acoustic intensity level is a logarithmic measure of the sound intensity (measured in W/m2), in comparison to the reference level of 10-12 W/m2.The measure of a ratio of two sound intensities is

I LI  10log10  dB (2.6) I0

where IIand 0 are the intensities.

The sound intensity level is denoted by LI and is measured in dB(dB is dimensionless),

-12 2 I0 is the standard reference sound intensity, where I0 = 10 W/m .

If IL, and IL, be the sound intensity and the sound intensity level at the distance r 1 I1 2 I2 1

and r2 from the point source then by using (2.5) and (2.6) we have

2 r1 II21 2 (2.7) r2

I L  10log1 dB (2.8) I1 10  I0

I L  10log2 dB (2.9) I2 10  I0

Combining the Eqs. (2.7) to (2.9) we have

1 r 2 LI10log1 dB I2 102 1 Ir02

Ir2 L 10log11 10log dB I2 10 10 2 Ir02

26 r LL20log1 dB (2.10) II21 10  r2

Eq. 2.10, Inverse square law, is implemented in the MATLAB function

‘Inverse_Square_Law_Calc’and is given by Table 2.1.

Table 2.1: Inverse_Square_Law_Calc

%********************************************************************** % Inverse Square Law Calculation %********************************************************************** % initial_distance = Distance from the source at which the % intensity level is known. % initial_intensity_level = The intensity level at a known distance. % distance = Distance of the point from the source at % which the intensity level need to be found. % intensity_level = The intensity level at the required % distance.

function [intensity_level,level_difference]= ... Inverse_square_law_Calc(initial_intensity_level,initial_distance, ... distance)

intensity_level=initial_intensity_level+20*log10(initial_distance/... distance);

level_difference= initial_intensity_level-intensity_level;

%------End of Function------

2.2 , INTENSITY AND THEIR LEVEL

2.2.1 SOUND PRESSURE

Sound pressure is the local pressure deviation from the ambient (average, or equilibrium) pressure caused by a sound . The SI unit for sound pressure is the Pascal (symbol:

Pa). The sound pressure deviation (instantaneous acoustic pressure) P is given by

F P  (2.11) A where F = Force, and A = Area

27 2.2.2 SOUND PRESSURE LEVEL

Sound pressure level (SPL) or sound level LP is a logarithmic measure of the rms sound pressure of a sound relative to a reference value. It is measured in (dB).

P LP  20log10  dB (2.12) P0

where P0 is the reference sound pressure and P is the rms sound pressure being measured. The commonly used reference sound pressure in air is = 20 µPa (rms).

2.2.3 RELATION BETWEEN SOUND PRESSURE AND SOUND INTENSITY

AND THEIR LEVELS

For a spherical sound source, the intensity, I r , in the radial direction is a function of distance, r , from the centre of the source and is given by

PP I ac ac (2.13) r Ar4 2

where Pac is the sound power and A the surface area of a sphere of radius . Thus the

1 1 sound intensity decreases with while the sound pressure decreases only with r 2 r

Hence, IP 2 (2.14)

Using (2.6) , (2.12) and (2.14) we have

IPP  2    LI 10log10  dB  10 log 10 2  dB  20log 10   dB=L P (2.15) IPP0   0   0 

There after by the help of Eqs. (2.6),(2.12), and (2.15) it is very convenient that if we know one of the value of Sound Pressure, Sound Intensity and their levels then other three can be easily obtained by the following way

28 Case I Case II

Sound Pressure P is known: Pressure Level LP is known:

P LP Pressure Level =LP  20log10  dB 20 P Sound pressure P0 10 0

Sound intensity Level LLIP L L I I 10 Sound intensityII 1010 Sound intensityII0 10 0

Case III Case IV

Sound Intensity I is known: Intensity Level LI is known: I L Intensity LevelLI 10log10  dB I I 10 0 Sound intensityII0 10

Pressure Level LL PI Pressure Level LLPI

L P LP Sound pressurePP 10 20 20 0 Sound pressurePP0 10

The above relations, conversion between Sound Pressure, Sound Intensity and their levels are implemented in the MATLAB function ‘Sound_pressure_level_Acoustic_intensity_le vel_Calc’ and are given in Table 2.2.

Table 2.2: Sound_pressure_level_Acoustic_intensity_level_Calc

%********************************************************************** % Sound Pressure,Pressure Level,Intensity and Intensity Level %********************************************************************** %r_pressure---> Refference Sound Pressure %r_intensity--> Refference Sound Intensity %s_pressure---> Sound Pressure %s_p_level----> Sound Pressure Level %a_intensity--> Sound Intensity %s_i_level----> Sound Intensity Level %option=1 ----> Sound Pressure is the Known Quantity %option=2 ----> Sound Pressure Level is the Known Quantity %option=3 ----> Sound Intensity is the Known Quantity %option=4 ----> Sound Intensity Level is the Known Quantity function [s_pressure,s_p_level,a_intensity,s_i_level]= ... Sound_pressure_level_Acoustic_intensity_level_Calc(s_pressure,r_pressur e,r_intensity,s_p_level,a_intensity,s_i_level,option)

%------CONTINUED------

29 if option == 1 s_p_level= 20*log10(s_pressure/(r_pressure*1e-6)); a_intensity= r_intensity*1e-12*10^(s_p_level/10); s_i_level= 10*log10(a_intensity/(r_intensity*1e-12)); end if option == 2 s_pressure= r_pressure*1e-6*10^(s_p_level/20); s_i_level= s_p_level; a_intensity= r_intensity*1e-12*10^(s_i_level/10); end if option == 3 s_i_level= 10*log10(a_intensity/(r_intensity*1e-12)); s_p_level= s_i_level; s_pressure= r_pressure*1e-6*10^(s_p_level/20); end if option == 4 a_intensity= r_intensity*1e-12*10^(s_i_level/10); s_p_level= s_i_level; s_pressure= r_pressure*1e-6*10^(s_p_level/20); end %------End of the Function------

2.3 ACOUSTIC POWER AND ACOUSTIC POWER LEVEL

Sound Power or Acoustic Power, Pacoustics , is a measure of Sonic Energy ( E ) per time (t unit). Its equivalent to Sound Intensity ( I ) times of the Area ( A ).It is measured in Watts.

PIAacoustics  . (2.16)

The measure of Sound power level is given by

P LP 10log 10  dB where PP, 0 are the sound powers. (2.17) P0

The Sound power level of a source is expressed in decibels (dB).The reference Sound

−12 power, P0 , in air is normally taken to be 10 watt. Sound power is neither room dependent nor distance dependent. Sound power belongs strictly to the sound source.

There after by the help of Eqs. (2.17) it is very convenient that if we know one of the value of the Acoustic Power or Sound Power Level then the other can be easily obtained by the following way

30 Case I Case II Acoustic Power P is known: Sound power level LP is known:

LP P  Sound power levelL 10log dB Acoustic powerPP 1010 W P 10  0 P0

The above relations, conversion between Acoustic Power and Sound Power Level are implemented in the MATLAB function ‘AcousticPower_to_AcousticPowerLevel_Calc’ and are given in Table 2.3.

Table 2.3: AcousticPower_to_AcousticPowerLevel_Calc %********************************************************************** % Acoustic Power and Acoustic Power Level Calulation %********************************************************************** %acoustic_power ---> Sound Power or Acoustic Power %s_p_level ---> Sound Power Level %r_s_power ---> Refference Sound Power Level %option1= ---> Acoustic Power To Sound Power Level %option2= ---> Sound Power Level To Acoustic Power function[acoustic_power,s_p_level]=AcousticPower_to_AcousticPowerLevel_ Calc(option,r_s_power,acoustic_power,s_p_level) if option == 1 s_p_level= 10*log10(acoustic_power/(r_s_power*1e-12)); end if option == 2 acoustic_power= r_s_power*1e-12*10^(s_p_level/10); end

%************************End of the Function***************************

2.4 PARTICLE VELOCITY AND PARTICLE VELOCITY LEVEL

As an propagates through a medium therefore the particle of the medium moves and hence we have a time dependent position and that is particle velocity.

The Particle velocity level or the sound velocity level tells the ratio of a sound incidence in comparison to a reference level of 0 dB in a medium; mostly air. It shows the ratio of

the particle velocity V and the particle velocity V0 .The Particle velocity level is given by

31 V LV  20log10  dB (2.18) V0

The Particle velocity level of a source is expressed in decibels (dB) The Reference

−8 particle velocity V0 is normally taken to be 5 × 10 m/s.

There after by the help of Eqs. (2.18) it is very convenient that if we know one of the value of the Particle Velocity and Particle Velocity Level then the other can be easily obtained by the following way

Case I Case II

Particle velocity V is a known: Particle Velocity Level LV is known:

LV V  Velocity Level =L  20log dB 20 V 10  Particle Velocity VV =0 10 m/s. V0

The above relations, conversion between Particle Velocity and Particle Velocity level are implemented in the MATLAB function ‘Particle_velocity2velocity_level_Calc’ and are given in Table 2.4.

Table2.4: Particle_velocity2velocity_level_calc %********************************************************************** % Particle Velocity to Particle Velocity Level %********************************************************************** %r_p_velocity---> Refference Partical velocity %p_velocity ---> Particle Velocity %p_v_level ---> Particle Velocity Level %option1= ---> Particle velocity to Particle velocity level %option2= ---> Particle velocity level to Particle velocity

function[r_p_velocity,p_velocity,p_v_level]=Particle_velocity2... velocity_level_Calc(r_p_velocity,p_velocity,p_v_level,option) if option == 1 p_v_level= 20*log10(p_velocity/r_p_velocity); end if option == 2 p_velocity= r_p_velocity*10^(p_v_level/20); end %------End of Function------

32 2.5 AND SOUND ENERGY LEVEL

The Sound energy level LW is given by

W LW  10log10  dB where W and W0 are the sound energy. (2.19) W0

The Sound energy level is expressed in decibels (dB) The Reference sound energy is normally taken to be 1 pJ or 10-12 J.

There after by the help of Eqs. (2.19) it is very convenient that if we know one of the value of the Sound Energy and Sound Energy Level then the other can be easily obtained by the following way

Case I Case II

Sound energy W is a known: Sound Energy Level LW is known:

LW W  Energy Level =L  10log dB. 10 W 10  Sound EnergyWW0 10 J. W0

The above relations, conversion between Sound Energy and Sound Energy Level are implemented in the MATLAB function ‘SoundEnergy2Energy_Level_Calc’ and are given in Table 2.5.

Table2.5: SoundEnergy2Energy_Level_Calc %********************************************************************* % Sound Energy to Sound Energy Level %********************************************************************* %r_s_energy ---> Refference Sound Energy %s_energy ---> Sound Energy %s_e_level ---> Sound Energy Level %option1= ---> Sound Energy to Sound Energy Level %option2= ---> Sound Energy Level to Sound Energy function [s_energy,s_e_level]= SoundEnergy2Energy_Level_Calc... (s_energy,s_e_level,r_s_energy,option) if option == 1 s_e_level= 10*log10(s_energy/(r_s_energy*1e-12)); end

33 if option == 2 s_energy= r_s_energy*1e-12*10^(s_e_level/10); end

%------End of the function------

2.6 AND SOUND DENSITY LEVEL

The Sound energy density level LE is given by

E LE  10log10 dB , where EEand 0 are the energy densities. (2.20) E0

The Sound energy density level is expressed in decibels (dB) and the Reference sound

3 -12 3 energy, E0 , is normally taken to be 1 pJ/m or 10 J/m .

There after by the help of Eqs. (2.20) it is very convenient that if we know one of the value of the sound energy density and energy density level then the other can be easily obtained by the following way

Case I Case II

Sound Energy E is a known: Energy Density Level LE is known:

LE E  Energy DensityLevel =L  10log dB. 10 E 10  EnergyDensityEE0 10 J. E0

The above relations, conversion between Sound Energy Density and Energy Density

Level are implemented in the MATLAB function ‘SoundEnergyDensity2Level_Calc’ and are given in Table 2.6.

Table2.6: SoundEnergyDensity2Level_Calc %********************************************************************* % Sound Energy Density to Sound Energy Density Level %********************************************************************* %r_se_density ---> Reference Sound Energy Density %s_energy_density ---> Sound Energy Density %s_density_level ---> Sound Energy Density Level %option=1 ---> Sound Energy Density to Sound Energy % Density Level

34 %option=2 ---> Sound Energy Density Level to Sound % Energy Density function [s_energy_density,s_density_level]= ... SoundEnergyDensity2Level_Calc(r_se_density,s_energy_density,s_density_l evel,option) if option == 1 s_density_level= 10*log10(s_energy_density/(r_se_density*... 1e-12)); end if option== 2 s_energy_density= r_se_density*1e-... 12*10^(s_density_level/10); end %------End of the Function------

2.7 LOUDNESS AND LOUDNESS LEVEL

2.7.1 LOUDNESS

The Sone is a unit of perceived loudness after a proposal of Stanley Smith Stevens

(1906-1973) in 1936. In , loudness is a subjective measure of the sound pressure. One sone is equivalent to 40 phons, which is defined as the loudness of a 1 kHz tone at 40 dBSPL. The number of sones to a phon was chosen so that a doubling of the number of sones to the human ear like a doubling of the loudness, which also corresponds to increasing the sound pressure level by 10 dB, or increasing the sound pressure by a factor 3.16 (= √10). At frequencies other than 1 kHz, the measurement in sones must be calibrated according to the frequency response of human hearing, which is of course a subjective process. The study of apparent loudness is included in the topic of psycho acoustics. Volume in acoustics is used as a synonym for loudness. It is a common term for the or the level of sound. The volume of a sound is a subjective perception. To "measure" loudness, the volume of a 1,000 Hz reference tone is adjusted until it is perceived by listeners to be equally as loud as the sound being "measured". The loudness level, in phons, of the sound is then equal to the sound-pressure level, in dB.

35 2.7.2 LOUDNESS LEVEL

The Phon is a unit of perceived loudness level, which is a subjective measure of the strength (not intensity) of a sound. At a frequency of 1 kHz, 1 phon is defined to be equal to 1 dB of sound pressure level above the nominal threshold of hearing, the sound pressure level SPL of 20 µPa = 2×10−5 Pa.

2.7.3 RELATIONS BETWEEN LOUDNESS AND LOUDNESS LEVEL

Loudness is not very easy to measure, and its determination requires ingenuity. The results of a great many experiments at different frequencies have been summarized by

Fletcher (op. cit.) and a graph representing the relationship between loudness and loudness level is given by Fig 2.1

.

Fig 2.1 Relations between loudness and loudness level

36 While the lower portion of the graph is noticeably curved, the portion in excess of 1 sone is straight. In the linear portion (corresponding to sounds from comfortably audible to unpleasantly loud), an increase in the loudness level on 9 phon is approximately equivalent to doubling the loudness.

Between the Loudness N in sone and the Loudness level LN in phon we have the following connection (ISO-recommendation ISO/R 131-1959):

LN  40 10 LoudnessNL  2 ,N  40 2.86 (2.21) LN  0.005 ,LN  40 40

Loudness level L = 10 log (N) + 40 ,N 1 N2 (2.22) = 40NN0.35 , 1

By using the Eqs. (2.21) and (2.22) we can easily find the value of any of the quantity loudness and loudness level if one of the values is known. These conversions are implemented in the MATLAB function ‘Loudness2LoudnessLevel_Calc’ and are given in Table 2.7.

Table2.7: Loudness2LoudnessLevel_Calc %********************************************************************* % Loudness TO Loudness Level calc %********************************************************************* %loudness ---> Loudness %loudness_level ---> Loudness Level %option1= ---> Loudness to Loudness Level %option2= ---> Loudness Level to Loudness function [loudness,loudness_level]= ... Loudness2LoudnessLevel_Calc(option,loudness,loudness_level) if option == 1 if loudness > 1 loudness_level = 10*log2(loudness)+ 40; end if loudness <= 1 loudness_level = 40*(loudness^0.35); end end

37 if option == 2 if loudness_level >= 40 loudness = 2^((loudness_level- 40)/10); %------CONTINUED------end if loudness_level < 40 loudness = (loudness_level/40)^2.86- 0.005; end end

%------End of Function------

2.8 LEVEL CHANGE AND THE LOUDNESS FACTOR

2.8.1 PSYCHOACOUSTICS

Level Change and Factor of Loudness per volume:

If Level change of loudness be L and the factor loudness be x then

L 10 L 10.log2  x and  x  2 . (2.23)

2.8.2 FIELD QUANTITY

Level Change and Factor of Sound pressure per voltage:

If Level change of sound pressure be P and the factor of sound pressure be y then

L 20 P 20.log10  y and  y  10 . (2.24)

2.8.3 ENERGY QUANTITY

Level Change and Factor of Acoustic intensity per power:

If Level change of acoustic intensity be I and the factor of acoustic intensity z then

L 10 I 10.log10  z and  z  10 . (2.25)

By using the Eqs. (2.23) (2.24) and (2.25) we can easily find the value of any of the two if one of the other values are known. These conversions are implemented in the

38 MATLAB function ‘Level_change_and_loudness_Factor_Calc’and are given in Table

2.8.

Table 2.8: Level_change_and_loudness_Factor_Calc

%********************************************************************** % Level change to Factor of loudness %********************************************************************** function[level,factor]= ... Level_change_and_loudness_Factor_Calc(option,level,factor)

%option 1---> For Psychoacoustics Level change to Factor of Loudness. %option 2---> For Psychoacoustics Factor of Loudness to Level change. %option 3---> For Field Quantity Level change to Factor of Pressure. %option 4---> For Field Quantity Factor of Pressure to Level change %option 5---> For Energy Quantity Level change to Factor of Intensity. %option 6---> For Energy Quantity Factor of Intensity to Level change. %======Psychoacoustics======if option == 1, factor= 2^(level/10); end if option == 2, level= 10*log2(factor); end %======Field Quantity======if option == 3, factor= 10^(level/20); end if option == 4, level= 20*log10(factor); end %======Energy Quantity======if option== 5, factor= 10^(level/10); end; if option== 6, level= 10*log10(factor); end %------End of Function------

2.9 OHM’S LAW AS ACOUSTIC EQUIVALENT

2.9.1 OHM'S ACOUSTIC LAW

Ohm's acoustic law sometimes called the acoustic phase law states that a musical sound is perceived by the ear as a set of a number of constituent pure harmonic tones. The law was proposed by physicist Georg Ohm in 1843. Hermann von Helmholtz elaborated the law into what is often today known as Ohm's acoustic law, by adding that the quality of a tone depends solely on the number and relative strength of its partial simple tones, and not on their relative phases. Helmholtz championed the law in opposition to contrary evidence expounded by August Seebeck.

The law has been interpreted as ‘a pitch corresponding to a certain frequency can only be

39 heard if the acoustical wave contains power at that frequency’ .Here we will find the relationship between the Acoustical quantities Sound pressure P , Particle velocityV ,

Acoustic impedance Z , and Sound intensity I .

2.9.2 SOUND PRESSURE

Sound pressure is the local pressure deviation from the ambient (average, or equilibrium) pressure caused by a sound wave. The SI unit for sound pressure is Pascal (Pa). The sound pressure deviation (instantaneous acoustic pressure) P is

F PFA, where  Force and  Area. (2.26) A

2.9.3 PARTICLE VELOCITY

Particle velocity (V ) is the velocity of a particle (real or imagined) in a medium as it transmits a wave. In many cases this is a of pressure as with sound, but it can also be a transverse wave as with vibration of a taut string. When applied to a sound wave through a medium of air, particle velocity would be the physical speed of an air molecule as it moves back and forth in the direction the sound wave is traveling as it passes. Particle velocity should not be confused with the speed of the wave as it passes through the medium, i.e. in the case of a sound wave; particle velocity is not the same as the .

2.9.4

The acoustic impedance or sound impedance, Z , is a frequency ( f ) dependent parameter and it has very useful meaning. Mathematically, it is the sound pressure, P , divided by the particle velocity ,V , and the surface area, S , through which an acoustic wave of frequency, f, propagates. Sometimes VS are referred to as the volume velocity

40 P i.eAcoustic ImpedanceZ (2.27) VS

The specific acoustic impedance z , is the ratio of sound pressure P , to particle velocity

V , at a single frequency.

P i.e Specific Acoustic Impedancez   ZS . (2.28) V

Using the relations (2.2), (2.11), and (2.28) we can conclude that the Sound Pressure (

P ), Sound Intensity ( I ), Sound Velocity (V ) and Acoustic Impedance ( Z ) are related in the following way.

Fig 2.2 Relation between Sound Pressure, Intensity, Impedance and Velocity

The above relations are implemented in the MATLAB function ‘Ohms_law_Calc’ and are given in the Table 2.9.

41 Table 2.9: Ohms_law_Calc

%********************************************************************** % Ohms Law Calculation %********************************************************************** function [pressure,velocity,intensity,impedance,text]= Ohms_law_Calc(pressure,velocity,intensity,impedance) if isempty(pressure)== 0 if isempty(velocity)== 0 intensity= pressure*velocity; impedance= intensity/(velocity)^2; text = 1; return end if isempty(impedance)== 0 velocity= pressure/impedance; intensity= pressure*velocity; text = 2; return end if isempty(intensity)== 0 velocity= intensity/pressure; impedance= ((pressure)^2)/intensity; text = 3; return end end if isempty(velocity) == 0 if isempty(impedance) == 0 pressure= velocity*impedance; intensity= pressure*velocity; text = 4; return end if isempty(intensity)== 0 pressure= intensity/velocity; impedance= pressure/velocity; text = 5; return end return end if isempty(impedance)== 0 if isempty(intensity)== 0 pressure= sqrt(intensity*impedance); velocity= pressure/impedance; text = 6; return end return end

%------End of the function------

42 2.10 ADDING ACOUSTIC LEVELS

Sound at a receiver is often the combination from two or more discrete sources. In general sources have different frequencies and random phase relation. These are called

Incoherent sources. Total energy from two incoherent sources equals the sum of the energy from each.(remember that intensity is proportional to P2).Since the total intensity is the sum of the intensity from each individual source, we can calculate the total pressure:

n 2 2 2 2 PPPPPT i 12  ......  n (2.29) i 1 and the total sound level P LP 20logT , where is the reference pressure PT 10 0 P0

2 PT  10log10  P0

n 1 2  10log10 2  Pi P0 i  1

LL n PPii 1 210 2 2 10 10log102  PPP 0 10 ,i 0 10 P0 i  1

L n P i 10  10log10  10 i  1

LL L PP12 Pn Therefore,L  10log 1010  10 10  ......  10 10 (2.30) PT 10   By using Eq. (2.30), we can easily add up the decibels. Here we add up to 10th level, using the MATLAB function ‘Combining_decibels_Calc’ and is given by Table 2.10.

43 Table 2.10: Combining_decibels_Calc

%********************************************************************** % Combining Decibels Calculation [up to 10th level] %********************************************************************** %'l1,l2,...l10' denotes the sound levels function[total_level]=... Combining_Decibels_Calc(l1,l2,l3,l4,l5,l6,l7,l8,l9,l10) if l1== 0 L1= 0; else L1= 10^(l1/10); end if l2== 0 L2= 0; else L2= 10^(l2/10); end if l3== 0 L3= 0; else L3= 10^(l2/10); end if l4== 0 L4= 0; else L4= 10^(l4/10); end if l5== 0 L5= 0; else L5= 10^(l5/10); end if l6== 0 L6= 0; else L6= 10^(l6/10); end if l7== 0 L7= 0; else L7= 10^(l7/10); end if l8== 0 L8= 0; else L8= 10^(l8/10); end if l9== 0 L9= 0; else L9= 10^(l9/10); end if l10== 0 L10= 0; else L10= 10^(l10/10); end total_level=10*log10(L1+ L2+ L3 + L4+ L5+ L6+ L7+ L8+ L9+ L10); %------End of Function------

44