, . . ( . . (1846 1915), ). , , , .
, , , (. 220). , , x t, . . x=x (, t).
. 220 , . , = 0, x(0, t)= coswt, , , t= x/v, v . , ,
x(x,t)=Acosw(t-x/v), (154.1)
, x (, t) , . (154.1) . ,
x(, t)=A cosw(t+x/v).
, , ,
x(x,t)=Acos[w(t -/v)+j0], (154.2)
= const , w , j0 , t, [w (t-x /v)+j0] .
k=2p/l=2p/vT=w/v. (154.3) (154.3), (154.2)
x(x,t)=A cos(wt-k+j0). (154.4)
, , (154.4) kx.
(140.7),
x(x,t)=Aei(wt-kx+j0),
(. 140).
, , . .
w(t-x/v)+j0=const. (154.5) (154.5) w,
dt -(1/v) dx=0,
dx/dt=v. (154.6)
, v (154.6) , , .
, , , ,
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x(r,t)=A0/rcos(wt-kr+j0), (154.7)
r . , , , 1 /r. (154.7) r, ( ).
(154.3) ,
v=w/k. (154.8)
, , , , .
v , D= 2/ x2 + 2/ y2 + 2/ z2 . (154.9) . , (154.9) , , (. (154.2)) (. (154.7)). , ,
, , . , , , . . () () .
, ; v v , , () (), , . v 0.
1. , ..v=v=0. v , l= vT=v/v 0. ,
n= v /l= v/(vT)=n 0
, v , , n0, .
2. , , .. v>0, v=0. v+v . ,
. . , , (v+v )/v .
3. , , .. v>0, v=0. , , , vT ( ) , . v T (.224), .. l'=l-v =(v-v ) ,
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. . v , , v/ (v-v ). 2 3, v<0 v <0, .
4. . , 2 3, , :
, , .
, , . v v , (159.1) .
, , . , , . , , , , . , , , ,
, k= 2p/l (. (154.3)), :
(157.2) , w = | 2 cos(2p/l)|, .
,
2px/l=mp (m=0, 1, 2,...), (157.3)
, 2 . ,
2px/l=(m+1/2)p (m=0,1,2,...),
(157.4)
. , (A =2 ), , , (A =0), . , , .
(157.3) (157.4) :
0 = l/2 ( m = 0, 1,2,...), (157.5)
=(+1/2)l/2 (m=0, 1, 2,...).
(157.6)
(157.5) (157.6) , l /2. l / 4.
, , ( (157.1) ), , ( (157.2) ). 2 cos (2px/l) , p, . . , , .
. , , . , , . , . , , , (. 222, ), (. 222, ). , , , , . , .
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, . , . ,
, . , , .
28. 29. -
- . , , , . DS (. 64) , . , , m 0 v-(-m 0 v)=2m 0 v, 0 , v . Dt DS , DS v D t (.64). n D Sv D t (n ).
, , ,
DS , . , 1/3 , (1/6) , . , , DS 1/6nDSvDt.
D = 2 m 0 v 1/6 n D Sv D t =1/3n m 0 v 2D S D t.
, ,
p =DP/(DtDS)=1/3nm0v2. (43.1)
V N ,
v 1, v 2,..., vN,
.
(43.1) (43.2)
= 1/30 <v>2. (43.3)
(43.3) - . -
.
, n = N/V,
.
m = Nm 0, (43.4)
pV =1/3m<v>2.
= ( ),
pV m=1/3M<v>2,
Vm . , , pVm=RT. ,
RT=1/3 <v>2,
= m0NA, m0 , N , (43.6) ,
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k = R/NA . , 480 /, 1900 /. 40 160 /.
<e0) =E/N = m0 <v> )2/2 = 3/2kT(43.8)
( (43.5) (43.7)) . , T=0 <e0> =0,
. . 0 , , . , (43.8) - .