Acoustics and Noise Control: 1119968

Introduction.

The subject of active noise control in relation to acoustics is very essential as it plays an important role in the reduction of unpleasant and unwanted noise sound generally termed as noise. There are very many problems in relation to noise control and other related problems. With improved technology and development, advantageous properties of actuators and Nosie controllers have been developed. With these techniques more effective and robust algorithms have thus been developed for the construction of noise controllers. Noise is physically manifested as a pressure wave and the pressure of sound energy cane be accurately measured. Difficulties are only experienced with regard to the measurement of acoustic energy.  The sound pressure ranges that the human era can hear is huge. The sound intensity level determination can be achieving through the use of the following formulae.

Through the use of these different formulas, the paper is aimed at effectively performing the mathematically calculation of the three problems.

Question one

1. Weighted L_p at 25m

Line source = 63 dB

1. For the point source,

But

1. For the line source

But

Sound power per unit length

For the point source

For the line source

• Internal dimensions

; has wall ceilings with low absorption

 High opening

Part a placed at center of building

Sound intensity in the plane of opening                           

 Center is at 5m

According to inverse proportional law, sound level L_p1 is measured at a distance r_1.

Sound L_p2 at a distance r₂ is thus;

          257

At 1m,

At 2m,

At 5m,

At 10m,

Question 2

1. The sound power dumper (LWA).

No background noise required corrections.

Microphone position	1	2	3	4	5	6
LAeq	70	64	64	64	61	61

The plan view is as illustrated in the following diagram.

The resulting sound power is calculating through the use of the following formulae.

The values of the noise power for the microphone positions are obtained as the root mean square values.

L refers to the distance between any two microphones used for the performance of the measurements (Khan et al., 2012). 

The microphone at position I root mean square value is obtained by using the formulae

Lpi = 10 lg [(tr 10^0.1Lri + tfº 10^0.1Lfi)/ (tr+ tf)

Lri is termed as the sound pressure level at the position I at the period tr

Lfi on the other hand refers to the sound pressure level at microphone position i during at the period for breaking denoted as tf (Khan et al., 2012).

Lw = Lp (10 m) + 20. Log (10) + 8 dBA (2)

= Lp(10 m) + 28 dBA

This is the formulae for the calculation of the sound power level for a point source for hemispherical emission.

The formula derived on the basis of the consideration of a spherical model f4or sound propagation for sources mainly in a ground plane.  The sound power levels are obtained through the consideration of the following important two formulas. Considering a case of 6 microphones as per this case of investigation. The second term is taken 11 instead of 8 for the hemispherical case.

Lpr1 = Lw + 20. log(r1) + 11 (for the spherical arrangement of the six microphones from the sound source of propagation).

 Lpr1 = Lp (r2) + 20.log(r2/r1)

The values of r indicate the distance of each of the six microphone from the sound source of propagation.

 For the position of the first microphone.

Lpr1 = Lp (r2) + 20.log(r2/r1),

For the microphone at position one, the value of Leq is obtained as 70.

70 denotes the continuous sound pressure level for the microphone at position 1.

Mathematically, the value of Leq can be obtained as

 For practical solutions, the values of Leq values can be taken within a minimum duration of 5 minutes. This is only possible if and only if enough vibrations are provided by the used microphone or for this case, the six microphones which were used for this case. Considering the case of six microphones which are used for this case, the equivalent leq for all the microphones can be obtained using the following formulae.

Replacing for all the values of Leq in the above equation, the mathematical equation becomes.

The microphones at positions 2, 3 and 4 are at the same power level. This is the same case with microphones at positions 5 and 6.

The equivalent value for the leq for the six position microphones is thus obtained as.

=71.39dB

• The obtained measured values relate effectively to the values which are obtained (Khan et al., 2012). This therefore a very effective method to obtain the power values as denoted in the article.

The above calculations were effectively obtained through the consideration of the following positions of the microphone. The calculated values as in a above have minimal differences in comparison to values that were initially values noted in the research article under BS 5228-1:20091. Tis therefore shows that through the employment of the formulae for the calculation of the sound power level in the case of six microphones are quite accurate and can easily be employed in other sound power levels analysis. The other information that can also be obtained from the measurements also include the radius or the position of the six microphones for the center of the sound propagation of the sound point source (Santoni et al., 2015). By effectively obtaining each position of the six microphones, the values of the distances can then be used to calculate the intensity of sound power for all the vibrations for the spherical model considerations (Shihab et al., 2017). The final term that can also be obtained from the measurements is the dumping of the vibrations as a results of the sound vibrations for all the six microphones. Through the evaluation of these different values the equivalent values of the sound power levels can then be obtained as noted in the above manipulations through the utilization of the equivalent values of all the six sound power level measurements for each of the six microphones.

The measurements cannot be effectively use in obtaining the values of sound pressure measurements for all the six microphones positioned in the spherical space (Tawfik, Soud, & Alwan, 2015). This is quite difficult considering the fact that most of the microphone are at the sound power levels. As seen in the measurements of the sound power levels for various six positions of the microphones. It is also very difficult to estimate the start and the end time of the measurements of the sound power levels for all the six cases of the microphones positions as outlined in the table measurements.

As seen the method effectively located the microphone positions and the values of L denoted the distances between two microphones.

For any hemispherical emission, the sound power level is determined as follows.

• The sound level generated by the dumper 30m away is calculated as

Lpr1 = Lp (r2) + 20. log(r2/r1)

The value of r2 is 30 m while the value of r1 is 10m

The value 10m is considered as the point source radius value for the calculations and the measurements. The consideration of the damper for the calculations is basically to aid in the ability of enhancing the control of the noise from the point sources through the sound energy dissipation (Santoni et al., 2015). This is a composition of resonate vibration energy absorption capability which is quite important in the enhancement of the reduction of the noise from the point sources.

The sound level is thus obtained as Lpr1 = 1.5dB + 20. Log (30/10)

As for all the formulations, the sound power level values are given in terms of decibels.

Sound power level= 11.02 Db

Questions 3

1. The wrong equation is the equation number 1, Lw = Lp + 10. Log (S) dBA

The stated equation is not the correct equation for the expression of sound power. It can be defined as the rate of transmission, reflection or the reception of sound energy. For this case of analysis, the transmission aspect of sound power is considered in the calculation of the values of sound power (Santoni et al., 2015). To validate the accuracy of this equation, it can be noted that a variation exists as the results obtained through the use of the equation results into wrong values of sound power. Sound power which is denoted by P is defined by the following equation (Bies, Hansen, & Howard, 2017). To state the correct equation for the calculation of the values of sound power, it is then simply reiterated using the following simple formulae that

F is defined as the sound force per unit vector, this is manipulated in consideration of the vector of propagation of the sound power values for every point sources considered in all the mathematical manipulation of the values of sound power intensities and levels for all the calculations.

V is the particle projection velocity. The velocities for the sound particles are therefore taken into consideration to derive the values of velocities at which the sound power particles are propagating for this case, free fields.

The correct formulae representation for the sound power is expressed through the use of the preceding formulae.

The surface area is defined by As and the source is fully encompassed by the area. This is termed as a new position for sound power level values. This value is obtained in reference to the point source power level values. Considering a sound source that is completely encompassed by the source. For a source situated in a free field over the reflecting surface (Kardous & Shaw, 2014). The equation is now expressed using the following formulae.  

The value of r is utilized in the same way to obtain the area value for which the sound power is acting.  The sound pressure level is denoted by Lp.

Ao is denoted by the term 1m^2.

The surface area of the hemisphere is denoted by the term

The formulae changes for the case of the hemisphere which is where all the six microphones have been positioned (Santoni et al., 2015). The surface area of a sphere is taken as , Using this formulae, the corresponding radius of the sphere can be rewritten as the subject of the formulae and is stated as

R=, The formulae can therefore be used in deriving the positions of the six microphone for the hemisphere case. After effectively deriving the positions of the sound power levels, values of sound power intensities can also be equivalently obtained Simon, F. (2018). 

The value of r must be quite efficient to enclose the sound power source as for the utilized example (Tawfik, Soud & Alwan, 2015). R is used in the calculation of the area value (Shihab et al.,  2017). The value of area is used in in obtaining the area for where the sound power intensity is acting as per the various formulations in the experiment. It can have reiterated that sound power intensity is calculated as

Sound power intensity=,

The value of r that was considered in the calculation of the area is termed the position of the sound power level in comparison to the point source.

The value of sound power is also seen to be independent of the distance from the sound source (Santoni et al., 2015).

The example is correct has it has effectively utilized the manufacturers sound pressure to obtain effective measurements of sound power and intensity parameters (Bies, Hansen, & Howard, 2017).

As obtained from the equation, the sound pressure has been effectively expressed through the use of the formulae Lw = 70 + 10. Log (630) = 98 dB

• The value of the sound pressure visa vie the source quite conforms to the theoretical reasoning with respect to the calculation of the values of sound pressure. The discrepancies in the sound pressure magnitudes have also been effectively elaborated as they mainly result from magnitude error.

The formulae that was used for the formulation was Lpr1 = Lp (r2) + 20. log(r2/r1). The distances r1 and r2 denoted the distance measurements from the point sources and are effectively used in the manipulation n for obtaining accurate pressure levels.

• The value of Lp as suggested by his article is obtained using the formulae (Rançon, 2018) .

The sound power levels estimated from single point by the author were obtained to be within 1.5dB.

Considering the formula.

Lpr1 = Lw + 20. log(r1) + 11 (8 for hemispherical), We use 11 for this manipulation because we are considering the case of microphone locations for spherical positions (Rançon, 2018).  

 Lpr1 = Lp (r2) + 20.log(r2/r1)

 Lpr1 = Lp(r2) + 20.log(r2/r1)

The value of Lp at 10 m is then calculated as

Lpr1 = 1.5dB+ 20.log (10/1)

=21.5 Db

The calculated value is varying minimally to the author’s projected value for Lp (Kardous, & Shaw, 2014). This variation is though minimal and can mainly attributed to magnitude measurements variations (Bies, Hansen, & Howard, 2017). The value therefore relates quite effectively to the value which is suggested by the author of the article.

References

Bies, D. A., Hansen, C., & Howard, C. (2017). Engineering noise control. CRC press.

Kardous, C. A., & Shaw, P. B. (2014). Evaluation of smartphone sound measurement applications. The Journal of the Acoustical Society of America, 135(4), EL186-EL192.

Khan, I., Muthusamy, D., Ahmad, W., Sällberg, B., Nilsson, K., Zackrisson, J., … & Håkansson, L. (2012). Performing active noise control and acoustic experiments remotely. International Journal of Online Engineering, 8(special issue 2), 65-74.

Karkulali, P., Mishra, H., Ukil, A., & Dauwels, J. (2016, October). Leak detection in gas distribution pipelines using acoustic impact monitoring. In IECON 2016-42nd Annual Conference of the IEEE Industrial Electronics Society (pp. 412-416). IEEE.

Rdzanek, W. J., & Rdzanek, W. J. (2014). The acoustic reactance of radiation of a planar annular membrane for axially-symmetric free vibrations. Archives of Acoustics, 24(2), 207-212.

Shihab, I. M., Soud, W. A., & Jebur, N. A. (2017). Theoretical and Experimental Study of the Vibration of a Drum Type Washing Machine at Different Speeds. Al-Nahrain Journal for Engineering Sciences, 20(5), 1160-1171.

Tawfik, M. A., Soud, W. A., & Alwan, R. S. (2015). The Effect of Soil Content, Drilling Parameters and Drilling Tool Diameter on the Vibration Assessment in the Drilling Rig. Al-Khwarizmi Engineering Journal, 11(1), 93-112.

Shihab, I. M., Soud, W. A., & Jebur, N. A. (2017). Theoretical and Experimental Study of the Vibration of a Drum Type Washing Machine at Different Speeds. Al-Nahrain Journal for Engineering Sciences, 20(5), 1160-1171.

Santoni, A., Bonfiglio, P., Fausti, P., & Martello, N. Z. (2015). Sound insulation of heavyweight walls with linings and additional layers: numerical investigation. In Euronoise (pp. 2537-2542). EAA-NAG-ABAV.

Simon, F. (2018). Long elastic open neck acoustic resonator for low frequency absorption. Journal of Sound and Vibration, 421, 1-16.

Rançon, J. (2018). La méthode verbo-tonale. Quel intérêt pour l’école d’aujourd’hui?