9 Principles of sound
声学原理
The abilities of speaking and hearing are very important
factors in our personal lives and in our environment.
Areas such as music, sound recording and reproduction,
noise control is also important.
波长
The main sources of environmental noise issues are
transportation noise,
industrial noise,
construction noise and
noise from leisure and entertainment.
Common topics of concern are
•
1）the exclusion of external noise 隔断外部噪声
•
2) the reduction of sound passing between
rooms and 减少房间之间的声音传递
•
3) the quality of sound inside rooms室内音质
Before these topics are studied , this chapter outlines
the basic principles of sound and its measurement.
These basic principles are indicated below:
9.1 Nature of sound 声音的特性
9.2 Sound levels 声级
9.3 Attenuation of sound 声音的衰减
9.4 Nature of hearing 听觉特征
9.1 Nature of sound
what is sound ?

Sound is a sensation produced in the ear and brain by
variations in the pressure of the air.

Sound is a Mechanical Wave. These pressure variations
transfer energy from a source of vibration .
What can be Origin of sound 声源?




Moving objects: loudspeakers扬声器, guitar strings吉他弦,
vibrating walls, and human vocal chords人声.
Moving air: horns号角, organ pipes 管风琴, mechanical fans风
机 and jet engines喷气发动机.
Vocal 声音的, 有声的, 歌唱的
Chord 弦, 和音, 情绪
How do the sound waves travel?

The sound waves travel in a longitudinal纵向的 type
Its corresponding Transverse Waves 横波
左右分工小能人(横波与纵波)
Water Waves
Water waves are an example of waves that
involve a combination of both longitudinal and
transverse
The sound waves can travel through solids, liquids and
gases
A vacuum?
Sound is a mechanical wave and cannot travel through a vacuum.
Light is an electromagnetic wave and can travel through the
vacuum of outer space
It is convenient to represent the wave as follows
plot（绘图） the vibrations
against time.
For a pure sound of one
frequency ，the plot takes the
form of a sine wave正弦波.
can be specified in terms of :
Wavelength
Frequency
Velocity
v  f 
How is the Velocity of sound?

The velocity of sound is affected by the properties of the
material through which it is traveling.

The velocity in air increases as the temperature or humidity
increases.

An indication of the velocity of sound in different materials is
given in table 9.1
P181
pine松树, 树木

5th row

Last row granite花岗岩
How is the Frequency of sound?

If an object that produces sound waves vibrate 100 times a
second, then the frequency of that sound wave will be ??
The human ear hears this as sound of a certain pitch音调.

Pitch is the frequency of a sound as perceived by human hear.

Low-pitched notes are caused
by low-frequency sound wave
high-pitched notes are caused
by high-frequency waves.
Note 笔记, 短信, 音符

The frequency range to which the human ear responds
is approximately 20 to 20, 000Hz
The range is too wide, what should we do?
To divided it into several parts
How to divide?
one method is

An octave band倍频程

Octave bands commonly used in frequency analysis have the
following centre frequencies.

31.5 63 125 250 500 1000 2000 4000 8000Hz
中心频率
63
125
250
500
1000
2000
4000
8000
45~
90
90~
180
180~
355
355~
710
710~
1400
1400~
2800
2800~5 5600~
600
11200
Hz
频率范围
Hz
Octave 八个一组的物品, 八度音阶
How to describe the Quality of sound 音质

sound with only one frequency.

sound with more than one frequency.

440Hz = fundamental基准音 or 1st harmonic谐音

880Hz = 1st overtone 泛音or 2nd harmonic

1320Hz = 2nd overtone or 3rd harmonic etc.

pure tone纯音
Overtones泛音 and harmonics谐音are frequencies equal to
whole-number multiples of the fundamental frequency

音调的高低取决于基频，而音色取决于谐频分量的构成
谐频harmonics
Basic frequency
880, 1320, 1760, 2200,
2640, 3080, 3520……
difference between pure tone, music and noise
When you sing in a bathroom, what would you find?
Resonance 声音的共鸣
Every object has a natural frequency
depends on factors such
as the shape, density and
stiffness of the subject.

Resonance occurs when the natural frequency of an
object coincides with the frequency of any vibrations
applied to the object.

The result of resonance is extra large vibrations at this
frequency.
9.1 Nature of sound
9.2 how to measure sound?
Sound power 声功率
Unit : watt
声源单位时间内向外辐射的声能
Sound intensity声强
Unit: w/m2
is the sound power distributed over unit area.
单位面积的声功率-单位时间单位面积所通过的声能
Sound pressure声压
Unit: Pa
is the average variation in atmospheric pressure caused by the
sound
声音所引起的空气压强的平均变化量
Intensity –pressure relationship
I
p
2
v
If you want to detect a sound at 1000Hz, it’s
sound intensity must be greater than
Io = 1X10-12 W/m2
Po = 20X10-6 Pa
Thresholds of hearing 听阈is the weakest
sound the average human ear can detect.


I = 100 w/m2
p =200 Pa
Thresholds of pain 痛阈 is the
strongest sound that the human ear
can tolerate.
What is Decibels ?分贝

Decibels is a logarithmic对数的ratio of two quantities.
I2
p2 2
N  10log10 ( )  10log10 ( )
I1
p1
Sound intensity level声强级
I
SIL  10log10 ( )
I0
Sound pressure level声压级
p
SPL  20log10 ( )
p0
I
p
2
v
Now, here is a question.
A clock with a alarm of 60dB
When there are two of such clocks,
Ring at the same time,
Do you think what the dB would be ?
Worked example 9.3
Calculate the change in sound level when the intensity of a
sound is doubled.
Let I=initial intensity , so 2I= final intensity
Let L1=initial sound level and L2=final sound level
 I  L = 3 dB
2I
L 2  L1  10log10 ( )  10log 
I0
 I0 
 2I I 
 10log    10log2  3
 I0 I0 
Therefore: double the energy gives a 3 dB increase in sound level
double the energy gives a 3 dB increase in sound level
decibels can be directly added?
decibels cannot be directly added?
Intensities can be added
L = 3 dB
I  I1  I2
Sound pressure can be directly added?
P P P
2
1
2
2
3dB increase in sound level is caused by doubling the
sound energy
10 dB increase in sound level seems approximately
twice as loud.
L = 3 dB
Worked example 8.4

Calculate the total sound level caused by the combination of
sound levels of 95dB and 90dB. Threshold of hearing intensity
=1X1-12W/m2

Let I1=intensity of 95dB
I2=intensity of 90dB and
I3=intensity of the combined sounds

Using
I
SIL  10log10 ( )
I0
I1
95  10log10 ( )
I0
I2
90  10log10 ( )
I0
I3  I1  I 2
I3
SIL  10log10 ( )
I0

Please check the following website
www.sengpielaudio.com/calculator

The addition of decibel values is made easier with
the aid of a scale such as that shown in figure 9.7.
3dB increase in sound level is caused by doubling the
sound energy
10 dB increase in sound level seems approximately
twice as loud.
L = 3 dB
9.3 can sound be attenuated 衰减
as spread out from a source?
their amplitude 振幅decreases and the sound level drops.
does the total energy of the sound wave decrease a lot?
Except for some absorption by the air, the total energy of the
wave nearly remains constant
but the area of the wave front constantly increases.
The energy therefore spreads over larger areas and the
density of this energy or the sound pressure measured at
any point must decrease.
9.3.1 How does a Point source attenuate?
Inverse Square Law 平方反比定律

The sound intensity from a point source of sound decreases
in inverse proportion to the square of the distance from the
source.
2
2
2
1
I1 d

I2 d
Worked example 9.5



A microphone measures sound at a position in a free field
5m from a point source. Calculate the change in SPL if the
microphone is moved to a position 10m from the source.
Let L1=SPL at distance d1=5m
L2=SPL at distance d2=10m
Using
 d2 
 102 
I
L1  L 2  10log( 1 )  10lo 22   10log 2   6
I2
5 
 d1 
The SPL decreases by 6 dB each time the distance is
double from a point source of sound in free space.
A roadway can be a line source of air and noise pollution and
need not be a straight line.
9.3.2 how does a Line source attenuate?
In free space
The attenuation of sound from a line source in a free field can be
shown by general relationship
I1 d 2

I 2 d1
Sound intensity from a line source decreases in simple inverse
proportion to the distance from the source.
Figure 9.9 Attenuation of sound from a line source
McMullan
9.4 Nature of hearing 听觉特性
9.4.1 do you know your ear?
can be divided into three main parts.
 Outer ear 外耳
 Middle ear 中耳
 Inner ear 内耳
9.4.2 longer exposure to noise, you may
have deafness耳聋
(1) Middle ear deafness 中耳耳聋
(2) Nerve deafness 神经性耳聋

Temporary threshold shift (TTS) 暂时性失聪
is a temporary loss of hearing which recovers in 1-2
days after the exposure to noise.

Permanent threshold shift (PTS)永久性失聪 is a
permanent loss of hearing caused by longer exposure
to noise.
9.4.4 how to judge the Loudness of a
sound？ 响度

a 50Hz tone at 70dB

a 50Hz tone at 85dB

a 50Hz tone at 78dB

a 1000Hz tone at 60dB

a 200Hz tone at 60dB
As the intensity of a sound increases
it is heard to be “louder”.
Which one is heard to be louder?
It
can be seen that the ear is most sensitive in the frequency
range between 2~5kHz , and least sensitive at low frequencies or
at extremely high frequencies.
The unit of loudness
a 50Hz tone at 78dB
a 1000Hz tone at 60dB
Their loudness are 60 phone
a 200Hz tone at 60dB
A sound with 60 phone is twice as loud as 30 phone?
Another unit:
sone is a renumbering重编号of the phone scale so that sone
values are directly proportional to the magnitude of the
loudness.
One sone is equivalent to 40 phons.
2 sones is twice as loud as 1 sone.
Sone is doubled each time the loudness level is increased by
10 phons
Exercises in class
1 The sound waves can travel through（
solids, liquids and gases
A solids
B liquids
C gases
D a vacuum
）
2 The frequency range to which the human ear
responds is approximately (
A 20 to 2,000Hz
B 20 to 20, 000Hz
C 200 to 2,000Hz
D 200 to 20,000Hz
)
3 double the energy gives a （
in sound level
A 3 dB
B 10 phones
C 6 dB
D 10 dB
） increase
4（
） increase in sound level seems
approximately twice as loud.
A 3 dB
B 10 phones
C 6 dB
D 10 dB
5 The SPL decreases by（
） each time the
distance is double from a point source of
sound in free space.
A 3 dB
B 10 phones
C 6 dB
D 10 dB
6 Sone is doubled each time the loudness
level is increased by (
)
A 3 dB
B 10 phones
C 6 dB
D 10 dB