21.
(longitudinal wave)
2.1
2.1.
(
/2
90
2.
2.1[Jerry D.Wilson]
2.1(m/s)
(0 C)
(100 C)
(0 C)
(0 C)
(0 C)
5100
3500
4500
5200
1850
1125
1400
1500
331
387
965
1284
316
1. vMRTP
= 1.40
R = 8.31 J/mol.K
M = 0.0288 kg/mol
P N/m2
kg/m3
2. v
Bulk modulus ( ) N/m2
kg/m3
3. vy
y Young , modulus N/m2
kg/m3
v = f
v t6.0331 v t C
m/s
v T t
T
v P ……………(1)
(P) = 1.01x105 N/m2
, = 1.29 kg/m3
, 40.1
0 C
0v smxx /08.33129.1
1001.140.1 5
V ,
R = 8.31 , T ,
m , M 1Mmn
PV = nRT
MRT
VRT
MmP
MRTP …………..(2)
40.1 , molkgxM /108.28 3
R = 8.317 J/mol K (2)
vmolkgx
KxTKmolJx/108.28
)()./317.8()40.1(3
v T1.20
(1)Mmn
Tv , Tkv tt v t tk 273 ……… …(3)
0 v 0 0273k
0vv t
2731
273273 tt
0vv t 2
1
)273
1( t
tv 21
0 )273
1( tv …………….(4)
....)1682
1()1(32
21 xxxx
21
2731 t
....273.211
2731
21
tt546
1 t
-40 C 40 C
21
2731 t
5461 t
(2) tv )546
1(331 t
tv t6.0331 ..……… (5)
v (N/m2)
(kg/m3)
1.
yv Y N/m2
kg/m3
2.
2
3. (Kundt’experiment)
(Kunt,s tube) 2.2
2.2
R l
D
R
. L
f l2
yl
vf21
y
2.2 d2 d
( ) fv =2df
(v)
3.
3.1(beats) 2
( ) 1 (beats
frequency ; f , fB)
7 10 = 21 fff
221 fff
2.3
40104
48
1 f1 2 f2
A
(1) tAy 11 sin
(2)
tAy 22 sin
y
)sin(sin 2121 ttyyY A
2sin
2cos2sinsin BABABA
ttAy )2
sin(])2
cos(2[ 2121
tff
tff
Ay )222
sin(])222
cos(2[ 2121
tff
tff
Ay )2
(2sin])2
(2cos2[ 2121
= 121
2fff
tfAy 11 2sin
1A ]2
)(2cos2[ 211 tffAA
tff
Ay )2
(2sin 211
)cos(2 212122
21 ttAAAAA
A )cos( 21 tt
)cos( 21 tt ntt 2)( 21
ntftf 222 21
tnff 21
tn
= 21 ffff B
221 fff
0.1 1 10
10 / 10 /
2.1 5 300
2 Hz
1 = f1
= f1/
f1 f2
1 f1 = 300 Hz , fB = 5 Hz , f2 = ?
fB = f1 - f2
5 = 300 – f2
f2 = 300 – 5 = 295 Hz
2 f2 = 295 Hz , fB = 2 Hz , f1/ = ?
fB = f1/ - f2
2 = f1/ - 295
f1/ = 297 Hz
fB = f2 - f1/
2 = 295 - f1/
f1/ = 293 Hz
2 = 295 Hz
= 293 Hz 293 Hz
2.2 600 0.5
0.5 1
1 25.01
HzfB 2
f1 = 600 Hz , f2 = ?
fB = f1 - f2
2 = 600 - f2
f2 = 598 Hz
fB = f2 - f1
2 = f1 - 600
f1 = 602 Hz
600 Hz 598 Hz
602 Hz
3.2
2.4 (P) (x)90
(P)
(x)
(P)
(x)
(1 loop) =2
2.4
3.3
(d )
0.1
0.1
(Echo) 20 C
2S = vt , mxtvs 05.17
2)206.0331(1.01.0
1.
2.
3.
S = vt S
v t
x x X h X
.
2.5 ..
S = v t
S = v t
= t
2.3 2 1 s 3 s 4 s
335 m/s
x
y
x
1 S = vt
2d1 = 331x1 ………………..(1)
y 3 2d2 = 335x3 ………………..(2)
(1)+(2) 2(d1+d2) = 335x4
d1+d2 = 670
= 670
3.4
2
1
1
2
2
1
2
1
2
1
sinsin
TT
nn
vv
1 = , 2 =
1 = , 2 =
v1 = , v2 =
T = t +273 , T t
1.
2.6
2.
2.7
2.7
3.
2.8
2.8
T , v
T , v
T , v
T , v
T
T
2.4
50 45
0.50 / (
)
µ×é¹
ÅÖ¡
vv ]
30sin45sin
µ×é¹
ÅÖ¡
vv
2/12/1
21
ÅÖ¡v
S
sh45sin
hs 2 S = vt
vth2 )50(2
21h
h = 25 m
25 2.5 T1 T2
1 2 1sin
2sin T1 = 1.0201T2 ( 2522)
T1 = 1.0201T2
2
1
2
1
sinsin
TT
01.10201.10201.1
sinsin
2
2
2
1
TT
3.52
2.9
. . . L d
2.9
nPsPs 21 ; n = 0 , 1 , 2 , 3,……………….
L d
nd sin ; n = 0 , 1 , 2 , 3,……………….
nLxd
nQsQs 21 ; n = 1 , 2 , 3,……………….
L d
)21(sin nd ; n = 1 , 2 , 3,……………….
)21(n
Lxd
Acoustic Interferometer
P
R r2
2.10
2.10
R
nrr 12 ; n = 0 , 1 , 2 ,3 ,…..
x
nxrr 212
R
)21(12 nrr ; n = 1 , 2 , 3 , …..
x
)21(212 nxrr
3.6 (resonance)
(natural frequency)
3.6.1
1. (Fundamental frequency)
2. (Overtone)
3. (Harmonic)
3.6.2 1
(stationary wave)
20 20,000
2.11
2.11 1 2.10 . L1
L2
41L 432L
21
12 LL
21
1 nn LL n = 1 , 2 , 3, ………… v = f
)(2 1 nn LL
vf
v , n = 1 , 2 , 3 ,…….
3.6.3 1
2.12
(a) L = /4 , f1 = v/4L
(b) L = 3( /4) , f2 = 3(v/4L) 1
( c) L = 5( /4) , f3 = 5(v/4L) 2
loop
124nL
Lvnvf
4)12(
n + 1
n = 1Lvf41 1
n = 2 )4(32 Lvf = 3f1 3 1
n = 3 )4(53 Lvf = 5f1 5 2
n = 4 )4(74 Lvf = 7f1 7 3
1 1 , 3 , 5 , 7 ,………
2.13 fundamental mode
3.6.4 2 2
(a) L = /2 , f1 = v/2L
(b) L = 2( /2) , f2 = 2(v/2L) 1
( c) L = 3( /2) , f3 = 3(v/2L) 2
loop
2.14
2
nL2
Lnvvf2
n + 1
n = 1Lvf21 1
n = 2 )2(22 Lvf = 2f1 2 1
n = 3 )2(33 Lvf = 3f1 3 2
n = 4 )2(44 Lvf = 4f1 4 3
1 , 2 ,3 ,4 ,……….
3.6.5
2.15 (a) L (b) 1 (c) 2 (d) 3
nL
n2
n = 1 , 2 ,3 ,……….
Lvnvf
nn 2
n = 1 , 2 ,3 , ………Tv
T =
=
TLnf n 2
n = 1 , 2 ,3 ,………
2.6
2 15 2 47
352 / ( 2543)
2 – 2 =2
21547
64 cm
v = 352 m/s , f = ?
fv
HzHzxsmvf 550
1064/3522
550 Hz
2.7 350 1.5 m
350 m/s
1 f = 350 Hz , l = 1.5 m v = .350 m/s , n = ?
2 lnvf2
)5.1(2)/350(350
msmnHz
n = 3
3 2 fv
mHzsm
fv 1
350/350
1 loop = 2
= ½ = 0.5 m
0.5 m 1 1.5 m
5.05.11x = 3
32.8 1
200 900 200 900
400 1 lop
lvnf2
n = 1 11 2
1 Tl
f ……….(1)
22 2
1 Tl
f ………..(2)
2
1
2
1
TT
ff
2
1
2
2
1
TT
ff
..………(3)
f1 = 200 Hz , f2 = 400 Hz , T1 = T , T2 = T + 900 N
900400
200 2
TT
NT 300
(1) 11 2
1 Tl
f
12
300
200x
31088.1 x kg/m = 1.88 g/m
3.7
AB
AB
AB = (node)
AB = 2 1 (N1)
AB = 3 2.16
(node) Q
path difference = n
AQ – BQ = n
. n = 1 , 2 , 3 , ……2.16
= 3
3.8 (Doppler effect)
2.17
2.17 ..
(Doppler effect)
2.17 . (f) ( )
(v)vf
1.( ) = vs
= fs = vs 2.18
t = 0 t = T t = T
2.181 ,
sfTt 1
1 ; d = vT =
1 ; ds = vsT
1
t = T/
2.15 / = d - ds = vT - vsT = (v - vs)T
s
s
fvv ………….(6)
(fo)vf o
/
sso vv
vff ………..(7)
2.
/ = d + ds = vT + vsT = (v + vs)T
s
s
fvv ………….(8)
(fo)vf o
/
sso vv
vff ………..(9)
(7) (9)
s
so vvvff ……….(10)
( – )
( + )
3. ( ) =
sfv
= v fs = fs
vo (s) 2.19
2.19 vo
( /)
/ = = vot = voT
v/ = v + vo …………(11)
f0 ( ) ;/vf o
v/
vvv
ff oso …………(12)
4.
v/ = v - vo …………..(13)/vf o
v/
vvv
ff oso …………. (14)
(12) (14)
vvv
ff oso ……………(15)
( + )
( +- )
s
oso vv
vvff ……………..(16)
(+vo –vs )
(-vo +vs )
2.7 96 km/hr
500 Hz 346 m/s
1.
2.
3.
4.
5. ( ) 7 m/s
6. ( ) 7 m/s
vs = 96 km/hr = 27 m/s , fs = 500 Hz , v = 346 m/s 1. = ?
=s
s
fvv
mHz
sm 638.0500
/27346/
2. = ?
=s
s
fvv
mHz
sm 746.0500
/27346/
3. fo
sso vv
vffsmsm
smHz/27/346
/346500
Hzf o 542
4. fo
sso vv
vffsmsm
smHz/27/346
/346500
Hzf o 464
5. vs = 0 , vo = 7 m/s , fo = ?
vvv
ff oso =
smsmsmHz
/346/7/346500 = 490 Hz
6. vs = 0 , ( ) vo = 7 m/s , fo = ?
vvv
ff oso
=sm
smsmHz/346
/7/346500 = 510 Hz
3.9 (Shock Wave)
(sonic boom)
(shock waves) 2.17
2.20 ( ) 2.20 ( )
2.17
v vs
ss vv
tvvtsin
, Mach number (M)
vvM s
sin1
(Mach number)
3
= h
A
B
C B
x h
x
2.21
ABCss vv
tvvtsin
BCDxhsin
xh
vv
s
2.8 510 m/s 6 km
340 m/s
.vs = 510 m/s , h = 6x103 m , v = 340 m/s
x = ?
xh
vv
s
sin
xh
vv
s
smsmmx
vhv
x s
/340)/510)(106( 3
kmmxx 9109 3
9 km
4.3
20 – 20000
4.1 - (sound intensity : I )
(P) (I)
(A): ( R )
API
24 RPI
10-12 - 1 W/m2
I0 = 10-12 W/m2
Imax = 1 W/m2
4.2 (sound intensity level ; )1 10-12 W/m2
1012
2.2
2.2
10-12 100 0
10-11 101 1
10-10 102 2
10-9 103 3
………… ………………. ………………..
10-1 1011 11
100 1012 12
4.3
I W/m2
I0 = 10-12 W/m2
(Intensity level ; )
0
log10II
db01010log10 12
12
db120101log10 12
1 2 I1 I2
0
2
0
121 log10log10
II
II
).(log102
0
0
121 I
III
2
121 log10
II
R1 R2 I1
I2
21
1 4 RPI , 2
22 4 R
PI
21
22
2
1
RR
II
2
121 log10
II
21
22
21 log10RR
2
1
221 log10
RR
1
221 log20
RR
nII0
1log10InI
n
4.4
(noise pollution)
2.3
2.3
( )
( )
7
7-8
8
91
90
80
4.5 (pitch)
(bass)
(trebel )
2.4
2.4
C(
)
D ( ) E ( ) F ( ) G
( )
A ( ) B ( ) C/ ( )
(
Hz)
256 288 320 341 384 427 480 512
C/ C C//
C/ C C/ C/ C// (octave)
4.6 [ ]
( quanlity of sound)
(overtones)
(fundamental)
2 , 3 , 5
1.5 ..
..
4.7.
2.22
(eardrum)
2.22
(cochlea)
2.23
2.23 . 2.23 . 2.23
2.23 . 40 Hz
60 dB 1,000 Hz 10 dB
( 2.23 . .) (threshold of hearing)
(threshold of pain)
4.8 2.24
2.24
20 20,000
4.8.1 (infrasound)
0.1 20
0.1
4.8.2 (ultrasound)
20
20 (ultrasound)
6x108
5x10-5
-
-
- 20 – 100 k Hz
20 – 100 kHz
-
-
(cavitation)
20 - 30
-
(echoenphalography)
- (ultrasonography)
(tranduser)
…….
Crummett , P., William and Western, B. Arthur. University Physics Models and Applications.
USA: McGraw-Hill, 1994
Cuttnell, John D. and Johnson, Kenneth W. Physics. USA: John Wiley & Sons, Inc.
2004
Giancoli, Douglas C. Physics Principle with Applications. USA: Prentice Hall. 1998
Halliday, Resnick and Walker. Fundamentals of Physics. USA: John Wiley & Sons, Inc. 2005
Reese, Ronald Lane. University Physics. USA: Brooks/Cole Publishing Company, 2000.
Sanny, Jeff and Moebs, William. University Physics. USA: The McGraw-Hill Companies, Inc.
1996
Serway , Raymond A., John W and Jewett, Jr. Physics for Scientists and engineers. USA:
Thomson Brooks/cole, 2004
Willson, Jerry D. College Physics. second edition ,USA: Prentice- Hall, Inc. 1994
. 1. 11
: , 2543.
. Concept Physics. : , 2537.
, .
.4.5.6. : ,
. .4.5.6 021 , 022 , 023 , 024 , 025 ,026. : ,
, , .
APPLIED PHYSICS 3 027. : , 2537.
. .5 3 027 3. :
, 2544.
. 3 027 ( .5 3). : , 2542
. 1 .
,
. MODERN COMPACT PHYSICS 1-6. :
, 2540.
, . 027. 2 :
, 2541.
. .5 3 027. : ,
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