Sound Waves
description
Transcript of Sound Waves
Sound WavesSound is a longitudinal wave in a mediumAudible range of human ear is 20 to 20000Hz
0
uF ma pA cA t
t
P1 P2
0
uF ma pA cA t
t
0
V A t u uV A t u
V A tc c
2 20 0
0
u Vp c c
c V
0 1 1
0 1
V A tc V A tc
V V V A t u
20
0 0 0
V V Bp c B c
V V
2 20 0
0
u Vp c c
c V
0
Vp B
V
Bulk
modulus
Please estimate the speed of sound in water, the bulk modulus of fresh water at 20oC is about 2.28×106 Pa.
A.150 B. 340 C. 710
D. 1480 E. 3000 m/s
63
0
2.18 101.48 10 /
1000
Bc m s
VdV
dpB pB
V
p
dV
dpVdppdV isothermal ,0
M
RTpv
pBV
p
dV
dpdVpVVdp
constpV
a
,0
.
1
空氣的 bulk modulus 若為等溫過程, pV=nRT ,
用此結果代入所得之聲速較實際值小。在聲音的傳遞,速度很快,空氣和周圍來不及做熱交換,要考慮絕熱過程,即
。
max( , ) cos( )y x t y kx t
max0
sin( )V A y
p B B Bky kx tV A x
Characteristic impedance or specific acoustic resistance
Energy in Wave Motion
( , ) ( , ) ( , )
( , ) ( , ) ( , )( , ) ( , )
P x t F x t v x t
P x t F x t v x tI p x t v x t
A A
The instantaneous rate of doing work at the point x and time t is
For sinusoidal wave with wave function given as
max( , ) cos( )y x t y kx t
The speed of the displacement would be
max( , ) / sin( )v x t dy dt y kx t
Energy in Wave Motion
( , ) ( , )I p x t v x t
The instantaneous rate of doing work at the point x and time t is
2 2max
2 2 20 max
sin ( )
sin ( )
I Bk y kx t
c y kx t
0
Bc
k
max( , ) sin( )v x t y kx t
max sin( )p Bky kx t
2 2 2max 0 max
1 1
2 2I Bkωy cω y
intensity of a sinusoidal sound wave
B
p
v
pI
22
2max
2max
0
logdB10I
Iβ
definition of sound intensity level
B
v max maxp Bky
Sound Velocity and Gauge Pressure
The maximum sound wave pressure human can tolerate is 28 Pa above the atmospheric pressure. Find the max displacement if frequency is 1000Hz. Given speed of sound is 344m/s
max
3
6
2
28
(343 / )(1.21 / )(2000 )
1.1 10 11
p py
v v f
Pa
m s kg m
m m
A.11 nm B. 0.11μm C. 11 μm
D. 0.11 mm E. 1.1 mm
Sound Attenuation
Why distant thunder is heard as a low rumble while nearby one is a higher
frequency crash.High or low frequency is better for
long distance communication?
Which thunder is heard as a higher frequency crash?
A. distant one B. nearby one C. same
Sound Attenuation
max sin( )p Bky kx t
Which material will have largest displacement under same sound pressure variation?
A. Steel B. Alumina C. water D. Air
Sources of Musical Sound
What factors would affect the frequency of sound generated from a guitar string?
The Doppler effect
Moving listener and stationary source
1 LL s
vf f
v
SS
LL f
vv
vvf
Moving source and moving listener
Shack Wave (Sonic Boom)
http://en.wikipedia.org/wiki/Sound_barrier
H.W. Estimate the speed of the fighter.
ttss
ttsttssss
tsstss
m
mm
mm
coscos2
)(),(
)(cos)(cos2coscos
cos ,cos
2121
2121
2121
2121
2121
2211
21beat
21beat 2
fff
2smcos't
拍音可利用來做樂器的調音。人類可感覺之拍音約 <7Hz
Beats Beats 拍音拍音
People used Doppler flow meter to measure the blood flow rates. The speed of sound in blood is known to be 1570 m/s and a typical red blood cell has a radius of 5μm. Please estimate what would be the frequency for the flow meter?
If the frequency shift measured by the Doppler flow meter is 100Hz (the meter was operated at 107Hz), please find the average velocity of blood flow.
A.3.5 mm/s B.1.5 cm/s C. 23 cm/s
D. 65 cm/s E. 120cm/s
G
v
橫波 (transverse wave) 彈性體所產生之形變為剪應變 (shear strain)
Y
v
縱波 (longitudinal wave) 彈性體所產生之形變為拉伸應變 (tensile strain) 恢復力為拉伸應力 (tensile stress)
m/s 3000kg/m1083.7
Pa103.833
10
G
v
(a) 鋼之密度為 7.83×103 kg/m3 , G=8.3×1010 Pa ,橫波在鋼中傳遞之速率為
(b) 鑽石的橫波聲速高達 12800 m/s ,密度為 3.51×103 kg/m3 ,他的 shear modulus 為
2vG =5.75×1011 Pa
Can bat tells what’s its prey?
The echo is modulated by the beating wing of prey, as a result, the motion of wings impose a “warble” to the echo.
Insect has its own characteristic flapping frequency
In air or water, which is easier to detect via Doppler shift?
The otolith organs are the primary means by which we sense linear acceleration of the head and the orientation of the head with respect to Earth's gravity. Each of these otolith organs contains a small sensory area known as a macula. Each macula contains several thousand vestibular hair cells. The cilia are embedded in a gelatinous matrix called the otolithic membrane. This membrane contains small piles of calcium carbonate crystals (CaCO3), called otoliths, a word which literally means "ear stones."
Hearing
Hearing
There is a problem for terrestrial animals.
In most animal, a change in pressure is heard
Energy propagation at interfaces.
Newton’s 3rd law at the interfaces
i r tp p p
i r tp p p
i r t
i t r
A A A
A A A
0 sin( )p c A kx t
sin sin
sini a a r a a
t w w
A c t A c t
A c t
i a a r a a t w wA c A c A c
w wr t i
a a
cA A A
c
2 a ai t
a a w w
cA A
c c
The amplitude of sound transmitted into water is only about 1/1800th that in air
i r t
i t r
A A A
A A A
w wr t i
a a
cA A A
c
2w w w wi t t i i t t
a a a a
c cA A A A A A A
c c
2
4 a a w wt i
a a w w
c cI I
c c
2 2 20 sin ( )I c A kx t 2 a a
i ta a w w
cA A
c c
2 2 2 22
2 22 2
4
4 4
a a a at w w t w w i
a a w w
a a w w a a w wa a i i
a a w w a a w w
c cI c A c A
c c
c c c cc A I
c c c c
2
4 a a w wt i
a a w w
c cI I
c c
The intensity of sound transmitted from air into water is about ?
A.50% B. 20% C. 1%
D. 0.1% E. 0.01%
How can terrestrial animal hear?
The Anatomy of Human Ear
A eardrum = 43mm2 A stirrup = 3.2 mm2 V fluid =1500m/s
PaB fluid91018.2 PaP earinner 4.0)max( mAinner
11104.4
http://www.sfu.ca/sca/Manuals/ZAAPf/e/equal_loud_cont.html
Sound Amplifier
When the size of an air bubble in water is smaller than sound wavelength, it can function as a sound amplifier
More realistic model is to treat the bubble as a damped oscillator system
/ 3600i t a a a w w w
a W
p p c A c A
A A