哈工程振动噪声--第6章 噪声控制的声学基础

6. 2 Basic Characteristics of Plane Sound Wave
The mass conservation equation The momentum equation
u 0 0 t x
u p 0 0 t x
The state equation
wavenumber (k) is defined as
k

c

2f 2 c
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授课人——柳贡民
2016年9月7日星期三
动力与能源工程学院 College of Power and Energy Engineering
Chapter 6 Fundamentals of Acoustics for Noise Control
P0 p 0 cons tan t P0 0 The grouping results from a Taylor-series expansion in 0 and neglecting the second-order and higher-order acoustic terms, leads to
(4) Frequency and Period
The number of pressure variations per second is called the frequency of the sound, in units of Hertz (Hz)
The reciprocal of the frequency of a pure tone is the period in seconds 20Hz – 20 kHz audible sounds fsound > 20kHz called ultrasounds (超声波) fsound < 20Hz called infrasounds (次声波） Dolphins and bats can emit ultrasonic waves.
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授课人——柳贡民
2016年9月7日星期三
动力与能源工程学院 College of Power and Energy Engineering
Chapter 6 Fundamentals of Acoustics for Noise Control
6. 1 The Wave Equation
page 4
授课人——柳贡民 2016年9月7日星期三
c RT
动力与能源工程学院 College of Power and Energy Engineering
Chapter 6 Fundamentals of Acoustics for Noise Control
6. 1 The Wave Equation
6. 1 The Wave Equation
推导理想流体媒质中的声波方程的四个基本假设:
1）媒质为理想流体，不存在粘性，无能量损耗； 2）媒质是均匀连续的，无声扰动时媒质在宏观上处于静止状态；
3）声波传播过程是绝热过程，压强仅是密度的函数，可以不考虑温度 的因素。因此可以用声压、质点振速和密度这三个参数来描述声场；
P

p
0
P 0
RT
p P0 0
P0 R 0T
Submitting the state equation of ideal gases into the speed function of sound wave
2 2 c0 RT p c
~ ~ ~U ( )0 t
~ D U ~ ~ P 0 Dt
The momentum equation (movement equation)
For the quiescent medium, neglecting the second-order and higher-order acoustic terms yields the linear acoustic equations The mass conservation equation
pe
1 T 2 p (t )dt 0 T
For harmonic waves, there are
pm pe 2
Here pm is the amplitude of sound pressure.
page 3
授课人——柳贡民
2016年9月7日星期三
动力与能源工程学院 College of Power and Energy Engineering
page 5
授课人——柳贡民 2016年9月7日星期三
动力与能源工程学院 College of Power and Energy Engineering
Chapter 6 Fundamentals of Acoustics for Noise Control
6. 1 The Wave Equation
(5) Wavelength
Wavelength is defined as the distance the pure-tone wave travels during a full period c cT f
From this equation we know that high frequency sounds have short wavelengths and low frequency sounds have long wavelengths.
6. 1 The Wave Equation
Acoustic disturbances can usually be regarded as smallamplitude perturbations to an ambient state ~ ~ ~ U U0 u P P0 p 0 The mass conservation equation (continuity equation)
第6章 噪声控制的声学基础
Chapter 6 Fundamentals of Acoustics for Noise Control
6. 1 The Wave Equation 6. 2 Basic Characteristics of Plane Sound Wave 6. 3 Acoustic Energy in Sound Field 6. 4 Sound Levels 6. 5 Radiation of Sound Source 6. 6 Sound Field in Rooms
p c
2
The 1-D Wave Equation
2 p 1 2 p 2 2 0 x 2 c0 t
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授课人——柳贡民 2016年9月7日星期三
动力与能源工程学院 College of Power and Energy Engineering
page 10
授课人——柳贡民
2 p
1 2 p c t
2 2
0
2 2 2 2 2 2 x y z
2
2016年9月7日星期三
动力与能源工程学院 College of Power and Energy Engineering
Chapter 6 Fundamentals of Acoustics for Noise Control
4）媒质中传播的是小振幅压力波，各声学参量都是一阶微量，远小于 平衡状态的参数。
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授课人——柳贡民
2016年9月7日星期三
动力与能源工程学院 College of Power and Energy Engineering
Chapter 6 Fundamentals of Acoustics for Noise Control
where is the specific heat ratio（比热比）, R is the specific gas constant（气体常数） for the gas, R=287 J/kg-K for air, and T is the absolute temperature of gas in degrees Kelvin, equal to 273.15 plus the temperature in degrees Celsius.
page 1
授课人——柳贡民
2016年9月7日星期三
动力与能源工程学院 College of Power and Energy Engineering
Chapter 6 Fundamentals of Acoustics for Noise Control
6. 1 The Wave Equation
The mass conservation equation The momentum equation The state equation
0 u 0 t
0
u p 0 t
p c2
The Wave Equation
The Laplacin operator for threedimensional problems is given
Chapter 6 Fundamentals of Acoustics for Noise Control
6. 1 The Wave Equation
(2) Particle Velocity（质点振速）
The acoustic particle velocity (u) is defined as the local motion of particles of fluid as a sound wave passes through the material. The acoustic pressure and particle velocity are related by the specific acoustic impedance（声阻抗率）: