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. : ,