10.6Homework Exercises

Exercise 10.1: Partition Wall

Two rooms are separated by a wall having a transmission coefficient equal to 0.063. If the SPL in Room 1 near the separating wall is 102 dB, what would the SPL be in the second room near the separating wall and away from it? The wall surface area is 15 m2, the average absorption coefficient of the second room is 0.4, and the total surface area is 200 m2.

(Answers): 85.6 [dB]; 80.5 [dB]

Exercise 10.2

Two rooms are separated with a wall having a transmission coefficient equal to 0.06. The separating wall surface area is 25 m2. The total surface area of the second room is 250 m2, and the average absorption coefficient of the second room is 0.3. If the SPL in Room 1 near the separating wall is 100 dB, determine:

(a)The SPL in the second room near the separating wall

(b)The SPL in the second room away from the separating wall

(Answers): (a) 84.8 [dB]; (b) 81.7 [dB]

Exercise 10.3

The total surface areas of Room 1 and Room 2 are 150 m2 and 200 m2, respectively. The two rooms are separated by a wall with a surface area of 15 m2 and having a transmission coefficient of 0.01. The average absorption coefficients of Room 1 and Room 2 are 0.4 and 0.3, respectively. If Room 1 contains a 0.1-watt isotropic noise source 2 meters away from the wall:

(a)What is the sound pressure level (Lp1 ) in Room 1 near the separating wall?

(b)What is the sound pressure level (L0p2) in Room 2 away from the separating wall?

(Answers): (a) 97.7739 dB; (b) 70.2042 dB

Exercise 10.4

(Answers): (a) 74.2 [m2], 269.6 [m2]; (b) 15.2 [dB]; (c) 91.1 [dB], 83.2 [dB]

Exercise 10.6: Double-Leaf Partition

A double-leaf partition divides a room into two smaller rooms. Room 1 contains a 2-watt isotropic noise source 2 meters away from the partition. Using the data provided in the table below:

(a)Calculate the noise reduction of the double-leaf partition.

(b)Calculate the insertion loss of the double-leaf partition.

Assume that:

1.When the dividing partition is not present, the average absorption coefficient of the surfaces, which previously belonged to Rooms 1 and 2, remains the same as listed in the table.

2.The total surface area of the new larger room is equal to the sum of the surface areas of Rooms 1 and 2.

3.The location for the sound pressure estimate necessary for insertion loss calculations, without the partition in place, is also 2 m away from the noise source (i.e., double-leaf partition thickness is negligible).

4.The acoustic pressure inside the partition cavity is uniform (i.e., same everywhere):

1 , 2

1 2

(Answers): (a) NR ¼ 42.7 [dB]; (b) IL ¼ 37.1 [dB].

Chapter 11

Power Transmission in Pipelines

This chapter and the next chapter introduce both analytical and numerical methods for filter designs. This chapter will focus on developing formulas of pressure and acoustic impedance in pipelines. These formulas are the foundation for analyzing sound waves in pipes. The next chapter will extend pipelines to pipes with side branches which can be used to design any complex pipe system.

Pipelines are pipes connected in series without any side branches. Pipes with side branches will be discussed in the next chapter. The complex amplitudes, acoustic impedance, balancing equations, and power transmission in pipelines will be covered in this chapter and are organized into the following sections:

Section 11.1 defines complex amplitudes of pressure. Four formulas (Formulas 2A–2D) for transferring complex amplitudes of pressure from one end of a pipe to the other end are introduced.

Section 11.2 defines acoustic impedance in a pipe considering both the forward and backward waves. The acoustic impedance is defined by the complex amplitude of pressure introduced in Section 11.1. Two formulas (Formulas 3A–3B) for calculating acoustic impedance from complex amplitudes of pressure are introduced.

Section 11.3 introduces two equations for (1) balancing pressure and (2) conservation of mass at the intersection between two pipes. Four formulas (Formulas 4A– 4D) for transferring complex amplitudes of pressure between two adjacent pipes are introduced.

Section 11.4 introduces a formula (Formula 5) for transferring acoustic impedances between two adjacent pipes.

Section 11.5 demonstrates two techniques for the frequency domain analysis of pipelines. The first technique is for calculating the equivalent acoustic impedance of pipelines (based on Formula 5). The second technique is for transferring the complex amplitudes of pressure in pipelines (based on Formulas 4A–4D). Example 11.4 shows the procedures for calculating power transmission coefficient of pipelines using a numerical approach. This example uses the computer program in Sect. 11.9.

Section 11.6 demonstrates a numerical method for modeling pipelines with three pipes in series. This method uses three MATLAB functions provided in the

H. Lin et al., Lecture Notes on Acoustics and Noise Control, https://doi.org/10.1007/978-3-030-88213-6_11