Chapter 14
SOUND
Sound waves（ 声波 ）
Planar waves
（平面波）
Wavefronts
Ray（ 波线 ）
S
Wavefronts
（ 波振面 ）
Spherical waves
（球面波）
Point source
波的几何描述：
Sound waves are longitudinal mechanical waves that can travel
through solids,liquids,or gases,The speed v of a sound wave in
a medium (having bulk modulus B（ 容变弹性模量 ） and
density?) is:
Bv?
VV
pB
/?
Where:
The speed of sound
(?p is change of pressure)
（ 纵波在媒质中的传播速度 ）
interference
S1 and s2 are point sources,
they are in phase,and same
wavelength,when they travel
through point P,the path
length difference:
L=? L2 -L1?
Ps1
s2 L2
L1
To relate phase difference? to path length
difference?L,we recall that a phase difference of
2? rad corresponds to one wavelength,So:
L
2 2
L
(1) When?=± 2m?,(m=0,1,2….)
we called fully constructive interference（相长干涉）,The two waves are in phase at p.
mL
(2) When?=± (2m+1)?,(m=0,1,2….)
we called fully destructive interference（相消干涉）,The two waves are out of phase at P.
2)12(
mL
Of course,two waves could produce intermediate
interference when?L is other value.
2L
18-5 Intensity and sound level（ 声强和声强级 ）
Density of medium
For spherical waves:
24 r
PI s
(1) Intensity and variation of intensity with distance:
For planner waves,I =a constant
22
2
1
m
a v ga v g yv
dtA
dE
A
PI
声强：声波的能流密度,
2212 W / m1W / m10
能够引起人们听觉的声强范围：
(2) The decibel scale（ 声强级 ）,
Consider I0=10-12W/m2 （ 人能听到的最小声音 ） is a standard
reference intensity,because it is near the lower limit of the
human range of hearing,the sound level（ 声强级 ） is
defined as:
0
lg10 II
For I = I0,? = 0
The unit of sound level is decibel (dB 分贝 ).
声强级：人们规定声强 （即相当于频率为 1000 Hz 的声波能引起听觉的最弱的声强）
为测定声强的标准,如某声波的声强为 I,则比值的对数，叫做相应于 I 的声强级,
2120 mW10I
0II
引起痛觉的声音炮 声铆 钉 机交通繁忙的街道通 常 谈 话耳 语引起听觉的最低声音树 叶 沙 沙声声 源 声强（ W m-2）
1
1
10-2
10-5
10-6
10-10
10-11
10-12
声强级 db
震耳响正常轻极轻
120
100
70
60
20
10
0
120
有的地方规定户外噪声不得超过 100分贝几种声音近似的声强、声强级和响度人耳的平均听觉范围（ the ear’s response）
人耳听觉的范围为 20~2000Hz.
20 1000500100 5000 10000
0
20
40
60
80
100
120
10-2
10-4
10-6
100
10-8
10-10
10-12
L/dbI/W/m2
HZ
痛阈 threshold
闻阈 threshold of hearing
语言区域
SOUND
Sound waves（ 声波 ）
Planar waves
（平面波）
Wavefronts
Ray（ 波线 ）
S
Wavefronts
（ 波振面 ）
Spherical waves
（球面波）
Point source
波的几何描述：
Sound waves are longitudinal mechanical waves that can travel
through solids,liquids,or gases,The speed v of a sound wave in
a medium (having bulk modulus B（ 容变弹性模量 ） and
density?) is:
Bv?
VV
pB
/?
Where:
The speed of sound
(?p is change of pressure)
（ 纵波在媒质中的传播速度 ）
interference
S1 and s2 are point sources,
they are in phase,and same
wavelength,when they travel
through point P,the path
length difference:
L=? L2 -L1?
Ps1
s2 L2
L1
To relate phase difference? to path length
difference?L,we recall that a phase difference of
2? rad corresponds to one wavelength,So:
L
2 2
L
(1) When?=± 2m?,(m=0,1,2….)
we called fully constructive interference（相长干涉）,The two waves are in phase at p.
mL
(2) When?=± (2m+1)?,(m=0,1,2….)
we called fully destructive interference（相消干涉）,The two waves are out of phase at P.
2)12(
mL
Of course,two waves could produce intermediate
interference when?L is other value.
2L
18-5 Intensity and sound level（ 声强和声强级 ）
Density of medium
For spherical waves:
24 r
PI s
(1) Intensity and variation of intensity with distance:
For planner waves,I =a constant
22
2
1
m
a v ga v g yv
dtA
dE
A
PI
声强：声波的能流密度,
2212 W / m1W / m10
能够引起人们听觉的声强范围：
(2) The decibel scale（ 声强级 ）,
Consider I0=10-12W/m2 （ 人能听到的最小声音 ） is a standard
reference intensity,because it is near the lower limit of the
human range of hearing,the sound level（ 声强级 ） is
defined as:
0
lg10 II
For I = I0,? = 0
The unit of sound level is decibel (dB 分贝 ).
声强级：人们规定声强 （即相当于频率为 1000 Hz 的声波能引起听觉的最弱的声强）
为测定声强的标准,如某声波的声强为 I,则比值的对数，叫做相应于 I 的声强级,
2120 mW10I
0II
引起痛觉的声音炮 声铆 钉 机交通繁忙的街道通 常 谈 话耳 语引起听觉的最低声音树 叶 沙 沙声声 源 声强（ W m-2）
1
1
10-2
10-5
10-6
10-10
10-11
10-12
声强级 db
震耳响正常轻极轻
120
100
70
60
20
10
0
120
有的地方规定户外噪声不得超过 100分贝几种声音近似的声强、声强级和响度人耳的平均听觉范围（ the ear’s response）
人耳听觉的范围为 20~2000Hz.
20 1000500100 5000 10000
0
20
40
60
80
100
120
10-2
10-4
10-6
100
10-8
10-10
10-12
L/dbI/W/m2
HZ
痛阈 threshold
闻阈 threshold of hearing
语言区域
