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Волны в упругой среде. Волновое уравнение

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IINEIANEEE AINOAeA?NOAAIIUE OIEAA?NEOAO EIAEAIA?IIE YEIEEIAEE.

IOeAI.

?AOA?AO II OECEEA

ia oaio

«Aieiu a oi?oaie n?aaea. Aieiiaia o?aaiaiea».

Auiieiee:

nooaeaio a?oiiu I-13

iaoeiino?ieoaeueiiai oaeoeueoaoa

Eaeeiei Aaea?ee.

I?aiiaeaaaoaeue:

Noaiaithe Aeaaeeneaa Ieeieaaae/.

a. Aeiiiaeaaeiai.

1999 aiae.NIAeA?AEAIEA.

no?.

Aeaaa I. Aieia.

§1. Iiiyoea oi?oaie aieiu. Iiia?a/iua e i?iaeieueiua aieiu.
……………………………… 2

§2. O?iio aieiu. Aeeeia aieiu.
………………………………………………………………
……………. 3

Aeaaa II. Aieiiaia o?aaiaiea.

§1. Iaoaiaoe/aneea naaaeaiey.
………………………………………………………………
………………. 4

§2. Oi?oaea aieiu a noa?aeia.

1) aieiiaia o?aaiaiea.
………………………………………………………………
…………………….. 5

§3. Oi?oaea aieiu a aacao e aeeaeeinoyo.

aieiiaia o?aaiaiea;
………………………………………………………………
…………………….. 8

neo/ae eaeaaeueiiai aaca
………………………………………………………………
…………………. 9

Nienie eniieueciaaiiie eeoa?aoo?u. ……….

Aeaaa I.

Aieia.

§1. Iiiyoea aieiu. Iiia?a/iua e i?iaeieueiua aieiu.

Anee a eaeii-eeai ianoa oi?oaie (oaa?aeie, aeeaeeie eee aaciia?aciie)
n?aaeu aicaoaeeoue eieaaaiey aa /anoeoe, oi aneaaenoaea acaeiiaeaenoaey
iaaeaeo /anoeoeaie yoi eieaaaiea aoaeao ?ani?ino?aiyoueny a n?aaea io
/anoeoeu e /anoeoea n iaeioi?ie nei?inoueth v. I?ioeann ?ani?ino?aiaiey
eieaaaiee a i?ino?ainoaa iacuaaaony aieiie.

*anoeoeu n?aaeu, a eioi?ie ?ani?ino?aiyaony aieia, ia aiaeaeathony
aieiie a iinooiaoaeueiia aeaeaeaiea, iie eeoue niaa?oatho eieaaaiey
ieiei naieo iieiaeaiee ?aaiiaaney. A caaeneiinoe io iai?aaeaiey
eieaaaiee /anoeoe ii ioiioaieth e iai?aaeaieth, a eioi?ii
?ani?ino?aiyaony aieia, ?acee/atho i?iaeieueiua e iiia?a/iua aieiu. A
i?iaeieueiie aieia /anoeoeu n?aaeu eieaaethony aaeieue iai?aaeaiey
?ani?ino?aiaiey aieiu. A iiia?a/iie aieia /anoeoeu n?aaeu eieaaethony a
iai?aaeaieyo, ia?iaiaeeeoey?iuo e iai?aaeaieth ?ani?ino?aiaiey aieiu.
Oi?oaea iiia?a/iua aieiu iiaoo aicieeiooue eeoue a n?aaea, iaeaaeathuae
nii?ioeaeaieai naeaeao. Iiyoiio a aeeaeeie e aaciia?aciie n?aaeao
aiciiaeii aicieeiiaaiea oieueei i?iaeieueiuo aiei. A oaa?aeie n?aaea
aiciiaeii aicieeiiaaiea eae i?iaeieueiuo, oae e iiia?a/iuo aiei.

?enoiie SEQ ?enoiie \* ARABIC 1

Ia ?en. 1 iieacaii aeaeaeaiea /anoeoe i?e ?ani?ino?aiaiee a n?aaea
iiia?a/iie aieiu. Iiia?aie 1, 2 e o. ae. iaicia/aiu /anoeoeu, ionoiyuea
ae?oa io ae?oaa ia ?annoiyiea, ?aaiia 1/4vO, o. a. ia ?annoiyiea,
i?ioiaeeiia aieiie ca /aoaa?oue ia?eiaea eieaaaiee,

niaa?oaaiuo /anoeoeaie. A iiiaio a?aiaie, i?eiyoue ca ioeaaie, aieia,
?ani?ino?aiyynue aaeieue ine neaaa iai?aai, aeinoeaea /anoeoeu 1,
aneaaenoaea /aai /anoeoea ia/aea niauaoueny ec iieiaeaiey ?aaiiaaney
aaa?o, oaeaeay ca niaie neaaeothuea /anoeoeu. Nionoy /aoaa?oue ia?eiaea
/anoeoea 1 aeinoeaaao e?aeiaai aa?oiaai iieiaeaiey; iaeiia?aiaiii
ia/eiaao niauaoueny ec iieiaeaiey ?aaiiaaney /anoeoea 2. Ii i?ioanoaee
aua /aoaa?oe ia?eiaea ia?aay /anoeoea aoaeao i?ioiaeeoue iieiaeaiea
?aaiiaaney, aeaeaaynue a iai?aaeaiee naa?oo aiec, aoi?ay /anoeoea
aeinoeaiao e?aeiaai aa?oiaai iieiaeaiey, a o?aouey /anoeoea ia/iao
niauaoueny aaa?o ec iieiaeaiey ?aaiiaaney. A iiiaio a?aiaie, ?aaiue O,
ia?aay /anoeoea caeii/eo iieiue oeeee eieaaaiey e aoaeao iaoiaeeoueny a
oaeii aea ninoiyiee aeaeaeaiey, eae e a ia/aeueiue iiiaio. Aieia e
iiiaioo a?aiaie T, i?ieaey iooue vO, aeinoeaiao /anoeoeu 5.

Ia ?en. 2 iieacaii aeaeaeaiea /anoeoe i?e ?ani?ino?aiaiee a n?aaea
i?iaeieueiie aieiu. Ana ?annoaeaeaiey, eanathueany iiaaaeaiey /anoeoe a
iiia?a/iie aieia, iiaoo auoue ioianaiu e e aeaiiiio neo/ath n caiaiie
niauaiee aaa?o e aiec niauaieyie ai?aai e aeaai. Ec ?enoiea aeaeii, /oi
i?e ?ani?ino?aiaiee i?iaeieueiie aieiu a n?aaea nicaeathony
/a?aaeothueany naouaiey e ?ac?aaeaiey /anoeoe (ianoa naouaiey /anoeoe
iaaaaeaiu ia ?enoiea ioieoe?ii), ia?aiauathueany a iai?aaeaiee
?ani?ino?aiaiey aieiu ni nei?inoueth v.

?enoiie SEQ ?enoiie \* ARABIC 2

§2. O?iio aieiu. Aeeeia aieiu.

Ia ?en. 1 e 2 iieacaiu eieaaaiey /anoeoe, iieiaeaiey ?aaiiaaney eioi?uo
eaaeao ia ine o. A aeaenoaeoaeueiinoe eieaaethony ia oieueei /anoeoeu,
?aniieiaeaiiua aaeieue ine o, a niaieoiiinoue /anoeoe, caeeth/aiiuo a
iaeioi?ii iauaia. ?ani?ino?aiyynue io enoi/ieea eieaaaiee, aieiiaie
i?ioeann ioaaouaaao ana iiaua e iiaua /anoe i?ino?ainoaa. Aaiiao?e/aneia
ianoi oi/ae, aei eioi?uo aeioiaeyo eieaaaiey e iiiaioo a?aiaie t,
iacuaaaony o?iioii aieiu (eee aieiiaui o?iioii). O?iio aieiu
i?aaenoaaeyao niaie oo iiaa?oiinoue, eioi?ay ioaeaeyao /anoue
i?ino?ainoaa, oaea aiaea/aiioth a aieiiaie i?ioeann, io iaeanoe, a
eioi?ie eieaaaiey aua ia aicieeee.

Aaiiao?e/aneia ianoi oi/ae, eieaaethueony a iaeeiaeiaie oaca, iacuaaaony
aieiiaie iiaa?oiinoueth. Aieiiaoth iiaa?oiinoue iiaeii i?iaanoe /a?ac
ethaoth oi/eo i?ino?ainoaa, ioaa/aiiiai aieiiaui i?ioeannii.
Neaaeiaaoaeueii, aieiiauo iiaa?oiinoae nouanoaoao aaneiia/iia
iiiaeanoai, a oi a?aiy eae aieiiaie o?iio eaaeaeue iiiaio a?aiaie
oieueei iaeei. Aieiiaua iiaa?oiinoe inoathony iaiiaeaeaeiuie. Aieiiaie
o?iio ana a?aiy ia?aiauaaony.

Aieiiaua iiaa?oiinoe iiaoo auoue ethaie oi?iu. A i?inoaeoeo neo/ayo iie
eiatho oi?io ieineinoe eee noa?u. Niioaaonoaaiii aieia a yoeo neo/ayo
iacuaaaony ieineie eee noa?e/aneie. A ieineie aieia aieiiaua iiaa?oiinoe
i?aaenoaaeytho niaie iiiaeanoai ia?aeeaeueiuo ae?oa ae?oao ieineinoae, a
noa?e/aneie aieia — iiiaeanoai eiioeaio?e/aneeo noa?.

?anniio?ei neo/ae, eiaaea ieineay aieia ?ani?ino?aiyaony aaeieue ine o.
Oiaaea ana oi/ee n?aaeu, iieiaeaiey ?aaiiaaney eioi?uo eiatho
iaeeiaeiaoth eii?aeeiaoo o (ii ?acee/iua cia/aiey eii?aeeiao y e z),
eieaaethony a iaeeiaeiaie oaca.

?enoiie SEQ ?enoiie \* ARABIC 3

(o, t) aeey iaeioi?iai oeene?iaaiiiai iiiaioa a?aiaie t. N oa/aieai
a?aiaie a?aoee ia?aiauaaony aaeieue ine o. Oaeie a?aoee iiaeii no?ieoue
eae aeey i?iaeieueiie, oae e aeey iiia?a/iie aieiu. A iaieo neo/ayo ii
auaeyaeeo iaeeiaeiai.

, ia eioi?ia ?ani?ino?aiyaony aieia ca a?aiy, ?aaiia ia?eiaeo eieaaaiee
/anoeoe n?aaeu, iacuaaaony aeeeiie aieiu. I/aaeaeii, /oi

=vO,
(1.1)

– /anoioa eieaaaiee), iieo/ei

=v
(1.2)

?anniio?aa e?aoei iniiaiua iiiyoey, naycaiiua n aieiie, ia?aeaeai e
iienaoaeueiie noi?iia, o.a. aieiiaiio o?aaiaieth.

Aeaaa II.

Aieiiaia o?aaiaiea.

§1. Iaoaiaoe/aneea naaaeaiey.

Yoio ia?aa?ao yaeyaony iaoaiaoe/aneei aaaaeaieai e oiio aeeiaie/aneiio
?anniio?aieth aiei, eioi?ia aoaeao aeaii a $2. ?anniio?ei i?iecaieueioth
ooieoeeth

f(at-bx)
(2.3) io a?aoiaioa at—bo.
I?iaeeooa?aioee?oai aa aeaaaeaeu ii t:

(2.4)

Caeanue oo?eo icia/aao aeeooa?aioee?iaaiea ii a?aoiaioo at—bx.
I?iaeeooa?aioee?oai oaia?ue iaoo ooieoeeth aeaaaeaeu ii o:

(2.5)

N?aaieaay (2.4) e (2.5), iu oaaaeaeaainy, /oi ooieoeey (2.3)
oaeiaeaoai?yao o?aaiaieth

(2.6)

aaea

u=a/b.

Eaaei aeaeaoue, /oi yoiio aea o?aaiaieth oaeiaeaoai?yao i?iecaieueiay
ooieoeey

f(at+bx)
(2.7)
(2.7) a?aoiaioa at+bx, a oaeaea noiia ooieoeee aeaea (2.3)
e (2.7).

Ooieoeee (2.3) e (2.7) ecia?aaeatho i?e iieiaeeoaeueiuo a, b ieineea
aieiu, ?ani?ino?aiythueany, ia aeaoi?ie?oynue, ni nei?inoueth e a
noi?iio niioaaonoaaiii aic?anoathueo eee oauaathueo cia/aiee o **).

O?aaiaiea (2.6)—aeeooa?aioeeaeueiia o?aaiaiea a /anoiuo i?iecaiaeiuo,
ea?athuaa a oeceea i/aiue aaaeioth ?ieue. Iii iacuaaaony aieiiaui
o?aaiaieai. A iaoaiaoe/aneeo eo?nao aeieacuaaaony, /oi iii ia eiaao
?aoaiee, ioee/iuo io oao, eioi?ua iiaoo auoue i?aaenoaaeaiu ooieoeeyie
aeaea (2.3) e (2.7) eee noia?iiceoeeae oaeeo ooieoeee, iai?eia?,

f1(at – bo) + f2(at+bx).

Anyeee ?ac, eiaaea ec oece/aneeo niia?aaeaiee iiaeii onoaiiaeoue, /oi oa
eee eiay oece/aneay aaee/eia s oaeiaeaoai?yao o?aaiaieth aeaea

(2.6a)

iu niiaeai ia iniiaaiee niiauaiiuo caeanue iaoaiaoe/aneeo naaaeaiee
caeeth/eoue, /oi i?ioeann eciaiaiee yoie aaee/eiu iineo oa?aeoa?
ieineie, aieiu, ?ani?ino?aiythuaeny a oo eee ae?oaoth noi?iio ni
nei?inoueth e, eee noia?iiceoeee oaeeo aiei.

Aeae ooieoeee f1, f2 ii?aaeaeyaony oa?aeoa?ii aeaeaeaiey enoi/ieea aiei,
a oaeaea yaeaieyie, i?ienoiaeyueie ia a?aieoea n?aaeu.

Ionoue enoi/ieeii aiei yaeyaony ieineinoue o=0, i?e/ai ia yoie ieineinoe
aaee/eia S eieaaeaony ii caeiio s =Acoswt. A yoii neo/aa io ieineinoe
o=0 ?ani?ino?aiythony ai?aai e aeaai aieiu

.

Ec eeiaeiinoe aieiiaiai o?aaiaiey neaaeoao, /oi anee aio oaeiaeaoai?ytho
ooieoeee s1, s2,s3, … a ioaeaeueiinoe, oi aio oaeiaeaoai?yao oaeaea
ooieoeey

S == S1 + S2 + S3 + …

(i?eioeei, noia?iiceoeee).

?anniio?ei ianeieueei i?eia?ia.

a) Aieiiaiio o?aaiaieth oaeiaeaoai?ytho neionieaeaeueiua aaaouea aieiu

s1 = Anis(wt — kx), s2= Acos(wt+kx).

Ia iniiaaiee i?eioeeia noia?iiceoeee aieiiaiio o?aaiaieth oaeiaeaoai?yao
noiy/ay aieia

s=2Acoskx coswt

yaeythuayny noia?iiceoeeae oieueei /oi ?anniio?aiiuo neionieaeaeueiuo
aaaoueo aiei.

a) Aieiiaiio o?aaiaieth ia iniiaaiee i?eioeeia noia?iiceoeee
oaeiaeaoai?yao anyeay ooieoeey aeaea

Yoi—ooieoeey aeaea f(at—bx); iia ecia?aaeaao ianeionieaeaeueioth aieio,
?ani?ino?aiythuothny aac aeaoi?iaoeee a noi?iio aic?anoathueo o.

a) Ionoue aieiu S1, S2, eiathuea aeae ei?ioeeo eiioeuenia,
?ani?ino?aiythony iaano?a/o iaeia ae?oaie. A iaeioi?ue iiiaio
iiiaioaeueiue nieiie noia?iiceoeee S1 + S2 yoeo aiei eiaao aeae,
iieacaiiue ia ?en. 4,a. *a?ac iaeioi?ia a?aiy iiiaioaeueiue nieiie aieiu
aoaeao eiaoue aeae, iieacaiiue ia ?en. 4, a, – aieiu i?ieaeoo «iaeia
neaicue ae?oaoth» e i?eoii eaaeaeay oae, eae aoaeoi ae?oaie ia
nouanoaoao.

§2. Oi?oaea aieiu a noa?aeia.

1. aieiiaia o?aaiaiea.

A i?aaeuaeouai ia?aa?aoa iu ?anniio?aee iaoaiaoe/aneoth noi?iio
aieiiaiai o?aaiaiey. A yoii aea ia?aa?aoa y oioae au ia eiie?aoiii
i?eia?a ?anniio?aoue eae ?aaioaao oio iaoaiaoe/aneee aiia?ao.

?enoiie SEQ ?enoiie \* ARABIC 4

– niauaiea oeaio?a oyaeanoe ?anniao?eaaaiiai eonea. Oiaaea

/aet2 aai oeaio?a oyaeanoe, ni?aaa – ?acoeueoe?othuay aiaoieo nee,
aeaenoaothuay ia eonie.

:

(2.7)

, iieo/ei o?aaiaiea

(2.8)

ni?aaaaeeeaia a eaaeaeie oi/ea noa?aeiy. Iii oeacuaaao, /oi onei?aiea
aeaiiie oi/ee i?iii?oeeiiaeueii /anoiie i?iecaiaeiie iai?yaeaiey ii ae a
yoie oi/ea.

Iiaenoaaeyy a (2.8) niioiioaiea (2.7), iieo/ei:

(2.9)

Aniiiiea oaia?ue oi?ioeo , niaea?aeauoth ii?aaeaeaiea aeaoi?iaoeee, e
iiaenoaaea aa a (2.9), iieo/aai:

(2.10)

Yoi—aieiiaia o?aaiaiea. Iii oeacuaaao, /oi niauaiea ?ani?ino?aiyaony ii
noa?aeith a aeaea aiei

(2.11)

eee ia?acoao noia?iiceoeeth oaeeo aiei. Nei?inoue ?ani?ino?aiaiey yoeo
aiei (nei?inoue caoea a noa?aeia)

(2.12)

(iu iioneaai aeey e?aoeinoe eiaeaen 0 o ?). Yoa nei?inoue oai aieueoa,
/ai aeano/a e /ai eaa/a iaoa?eae. Oi?ioea (2.12)—iaeia ec iniiaiuo
oi?ioe aeonoeee.

, n eioi?ie

. Aeeooa?aioee?oy (2.11) ii t e ii x, iieo/aai:

ut)
(2.13a)

ut),
(2.13a)

ut).
(2.13a)

Oaeei ia?acii, niauaiea, nei?inoue, aeaoi?iaoeey e iai?yaeaiea
?ani?ino?aiythony a aeaea naycaiiuo ii?aaeaeaiiui ia?acii iaaeaeo niaie
iaaeaoi?ie?othueony aiei, eiathueo iaeio e oo aea nei?inoue e
iaeeiaeiaia iai?aaeaiea ?ani?ino?aiaiey.

ut). Oece/aneay eioa?i?aoaoeey caeanue i/aaeaeia: ieiei iaeneioia eee
ieieioia niauaiey ninaaeiea (aaneiia/ii aeeceea) oi/ee iaeeiaeiai
niauaiu e, neaaeiaaoaeueii, iao ie ?anoyaeaiey, ie naeaoey; a oio
iiiaio, eiaaea niauaiea aeinoeaaao iaeneioia (ieieioia), aai aic?anoaiea
niaiyaony oauaaieai (eee iaiai?io).

N?aaieaay oi?ioeu (2.13a), (2.13a) e i?eieiay ai aieiaiea (2.12) iu
aeaeei, /oi

(2.14)

aaea

(2.15)

naycaii n oi?iaeueiie aiaeiaeae iaaeaeo o?aaiaieyie (2.14) e caeiiii
Iia (? aiaeiae/ii ?aciinoe iioaioeeaeia, v – neea oiea).

§ 2. Oi?oaea aieiu a aacao e aeeaeeinoyo

Aieiiaia o?aaiaiea.

iu caeanue iiieiaai (eae e a § 1) iauaa niauaiea aauanoaa,
caiieiythuaai iauai, caeeth/athuee a naaa i/aiue iiiai aoiiia, ii iaeue
ii n?aaiaieth n aeeeiie aieiu.

Aoaeai n/eoaoue, /oi ?anniao?eaaaiue aac eee aeeaeeinoue iaoiaeyony a
i/aiue aeeeiiie oeeeeiae?e/aneie o?oaa, ia?acothuea eioi?ie ia?aeeaeueiu
ine o, e /oi niauaiea caaeneo oieueei io iaeiie eii?aeeiaou o. Iu iiaeai
i?eiaieoue e noieao aaca eee aeeaeeinoe, caiieiythuaio o?oao, oa aea
?annoaeaeaiey, /oi e e noa?aeith (§ 1). Iu i?eaeai, oaeei ia?acii, e
o?aaiaieth

(2.16)

ia caaenyo ie io o, ie io t.

O?aaiaiea (2.16) i?eiaieii e a neo/aa ieineeo aiei a iaia?aie/aiiie
aeeaeeie eee aaciia?aciie n?aaea (iiaeii iuneaiii auaeaeeoue
oeeeeiae?e/aneee noiea, ia?aeeaeueiue iai?aaeaieth ?ani?ino?aiaiey e
i?eiaieoue e iaio oa aea ?annoaeaeaiey, /oi e noieao, caeeth/aiiiio a
o?oaa).

Eae ecaanoii ec oa?iiaeeiaieee, ? anoue ooieoeey ieioiinoe aeaiiie iannu
aaca (eee aeeaeeinoe) e aa oaiia?aoo?u. Oaiia?aoo?a a naith i/a?aaeue
eciaiyaony i?e naeaoee e ?ac?aaeaiee. Oaieii?iaiaeiinoue aacia e
aeeaeeinoae i/aiue iaea, iiyoiio iiaeii n/eoaoue a ia?aii i?eaeeaeaiee,
/oi i?e ?ani?ino?aiaiee caoea i?ioeann naeaoey e ?ac?aaeaiey eaaeaeie
/anoe aaca eee aeeaeeinoe i?ienoiaeeo aaeeaaaoe/anee, o. a. aac
caiaoiiai oaieiiaiaia n ninaaeieie /anoyie. A oa?iiaeeiaieea
iieacuaaaony, /oi a yoii neo/aa (anee iiaeii i?aiaa?a/ue aioo?aiiei
o?aieai e iaeioi?uie ae?oaeie yaeaieyie oaiia?aoo?a yaeyaony
iaeiicia/iie ooieoeeae ieioiinoe , e neaaeiaaoaeueii, aeaaeaiea oaeaea.

a oaa?aeii oaea oaeaea caaeneo io oaiia?aoo?u. Ii a aeonoeea oaa?aeuo
oae yoi ianoiyoaeuenoai ia ea?aao, nouanoaaiiie ?iee.

A aacao e a aeeaeeinoyo ca iaeioi?uie eneeth/aieyie (iai?eia? aiaea, i?e
oaiia?aoo?a ieaea 4° N) oaiia?aoo?a ?anoao i?e naeaoee e oiaiueoaaony
i?e ?anoe?aiee.

Anoue iaeiicia/iay ooieoeey ieioiinoe:

p=f(p).
(2.17)

Aaaaeai iaicia/aiey

— niioaaonoaaiii eciaiaiey aeaaeaiey e ieioiinoe i?e ia?ooaiee
?aaiiaaney.

Iiaenoaaeyy ia?aoth oi?ioeo (2.18) a (2.16) e i?eieiay ai aieiaiea, /oi
i?e ?aaiiaanee aeaaeaiea ia caaeneo io o, o. a.

iieo/aai:

(2.19)

:

a) Iiaenoaaeyy (6.28) a (6.27), eiaai:

)

,

)2……

), oi iieo/aai:

)2…..
(2.20)

)3, . . ., e caiaieoue (2.20) eeiaeiui niioiioaieai

Oai naiui iu ia?aie/eaaai naay enneaaeiaaieai aiei iaeie eioaineaiinoe.

) —iinoiyiiue i?e aeaiiuo oneiaeyo iiuoa eiyooeoeeaio, ii?aaeaeyaiue
ninoiyieai n?aaeu i?e ?aaiiaanee.

a) Iauai V0 a ?acoeueoaoa aeaoi?iaoeee i?aa?auaaony a iauai

),
(2.21)

oae eae caeanue iiia?a/iue ?acia? (a ioee/ea io oaa?aeiai noa?aeiy)
inoaaony, iinoiyiiui, a aeeeia i?aa?auaaony a .
Ii i?iecaaaeaiea ieioiinoe ia iauai, ?aaiia ianna ?anniao?eaaaiie
ii?oeee aauanoaa, ia iaiyaony:

Iiaenoaaeyy (2.18) e (2.21), iieo/aai:

I?aiaa?aaay e caeanue aunoeie noaiaiyie iaeie aaee/eiu ,
iieo/aai:

Oaeei ia?acii,

(2.22)

Iiaenoaaeyy, iaeiiaoe, (2.22) a (2.19), iu iieo/aai aieiiaia o?aaiaiea

(2.23)

(2.24)

Ionthaea caeeth/aai, /oi ?anniao?eaaaiua iaeua aeaoi?iaoeee
?ani?ino?aiythony a aeaea ieineeo ia aeaoi?ie?othueony aiei; nei?inoue
?ani?ino?aiaiey (nei?inoue caoea) oai aieueoa, /ai neeueiia a aeaiiie
n?aaea aic?anoaao aeaaeaiea i?e aaeeaaaoe/aneii aic?anoaiee ieioiinoe;
iia ?aeia eaaae?aoiiio ei?ith ec i?iecaiaeiie aeaaeaiey ii ieioiinoe,
acyoie i?e cia/aiee iineaaeiae a ionoonoaea aieiu ( ).

2. Neo/ae eaeaaeueiiai aaca. Eaeaaeueiui aacii iacuaaaony aac, aeey
eioi?iai ni?aaaaeeeai o?aaiaiea ninoiyiey

pV=RT,
(2.25)

aaea p – aeaaeaiea, V—iauai iaeiiai iiey, R—oieaa?naeueiay aaciaay
iinoiyiiay, ?aaiay 8,3143 y?a/a?aae, T—oaiia?aoo?a, ecia?aiiay ii
oa?iiaeeiaie/aneie oeaea («aaniethoiay oaiia?aoo?a»), eee

aaea I— ianna 1 iiey, = M/V— ieioiinoue.

Aicaeoo, eenei?iae, acio, aiaei?iae e iiiaea ae?oaea aacu i?e eiiiaoiie
oaiia?aoo?a e aeaaeaiee ii?yaeea aoiinoa?iiai iiaeii ?anniao?eaaoue n
aeinoaoi/iui aeey aeonoeee i?eaeeaeaieai eae eaeaaeueiua aacu.

Eae o/eo oa?iiaeeiaieea, a neo/aa eaeaaeueiiai aaca niioiioaiea (2.17)
eiaao aeae

(2.26)

aaea

iinoiyiiay aaee/eia (N e N — oaieiaieinoe aaca niioaaonoaaiii i?e
iinoiyiiii aeaaeaiee e iinoiyiiii iauaia). Neaaeiaaoaeueii, caeanue

(2.27)

(oi?ioea Eaieana).

Aua caaeieai aei Eaieana aii?inii i nei?inoe caoea a aicaeooa caieiaeny
Iuethoii. Ii n/eoae, /oi

(2.26a)

o. a. ia o/eouaae eciaiaiey oaiia?aoo?u aicaeooa i?e ?ani?ino?aiaiee a
iai caoeiaie aieiu, aneaaenoaea /aai iieo/ee aeey nei?inoe caoea
niioiioaiea

(2.27a)

Yoi niioiioaiea iiaeii iieo/eoue ec o?aaiaiey (2.24), iiaenoaaeyy a iaai
(2.26a) aianoi (2.26).

Aeey aicaeooa ( =1,4) i?e eiiiaoiie oaiia?aoo?a (20° N, O =293°)
oi?ioea Iuethoiia aeaao u =290 i/nae, oi?ioea Eaieana e =340 i/nae.
N?aaieaay yoe cia/aiey n oaie, eioi?ua aeaao iiuo (ae. V, § 3), iu
aeaeei, /oi oi?ioea Eaieana, a ioee/ea io oi?ioeu Iuethoiia, oi?ioi
niaeanoaony n iiuoii. Oi?ioea Eaieana oi?ioi iiaeoaa?aeaeaaony ia iiuoa
e aeey ae?oaeo aacia (ii e?aeiae ia?a i?e ia i/aiue aunieeo /anoioao.

Yoei ii?aaaeuaaaony i?aaeiieiaeaiea i oii, /oi naeaoea e ?ac?aaeaiea
aaca a caoeiaie aieia yaeythony i?aeoe/anee aaeeaaaoe/aneeie
i?ioeannaie.

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