Ответы (1115944), страница 7

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Dx =. IjbfZeuom]eZo dx ≈ Fdϕ , ]^_F±nhdmkdλgh_jZkklhygb_kh[bjZxs_cebgauihwlhfm Dx ≈ FDϕ .JZaj_rZxsZykihkh[ghklv±hlghr_gb_baf_jy_fhc^ebgu\hegudfbgbfZevghcjZagbp_^ebg\hegjZaj_rZ_fhc^Zggufijb[hjhfKh]eZkghdjbl_jbxJwe_y^\_\hegu^ebgudhlhjuojZaebqZxlkygZδλfh]ml[ulvjZaj_r_gu\kemqZ__kebfZdkbfmf^eyh^ghcbaλ1gbokh\iZ^Z_lkfbgbfmfhf^ey^jm]hclh_klv m ( λ + δλmin ) =  m +  λ ⇒ δλmin =, ihNmNwlhfm jZaj_rZxsZy kihkh[ghklv ^bnjZdpbhgghc j_rzldb \ ki_dlj_ m]h ihjy^dZ R = mN .LZdbfh[jZahfjZaj_rZxsZykihkh[ghklvj_rzldbm\_ebqb\Z_lkykm\_ebq_gb_fqbkeZs_e_c h^gZdh g_h]jZgbq_ggh_ m\_ebq_gb_ qbkeZ s_e_c g_\hafh`gh baaZ ihl_jb dh]_j_glghklb^bnjZ]bjh\Z\rboemq_cIheyjbaZpby\hegIjhoh`^_gb__kl_kl\_ggh]hbiehkdhiheyjbah\Zggh]hk\_lZ q_j_a b^_Zevguc b g_b^_Zevguc iheyjhb^u AZdhg FZexkZ Kl_i_gv iheyjbaZpbb\heg IheyjbaZpby \heg ijb ba[bjZl_evghf ih]ehs_gbb AZdhg ;m]_jZEZf[_jlZ;_jZ1) IheyjbaZpby\heg:IheyjbaZpby\hegu±gZjmr_gb_kbff_ljbbjZkij_^_e_gby\hafms_gbchlghkbl_evghgZijZ\e_gby jZkijhkljZg_gby \hegu Hq_\b^gh qlh iheyjbaZpby \hafh`gZ lhevdh ^ey ih31i_j_qguo\heg kf we_dljhfZ]gblgu_ \hegu ©ZgZeh]bqguª ihi_j_qguf gZijZ\e_gb_dhe_[Zgbc i_ji_g^bdmeyjgh d kdhjhklb ihwlhfm hgb lZd`_ fh]ml [ulv iheyjbah\Zgu <\hegZobkimkdZ_fuobklhqgbdZfbk\_lZgZijZ\e_gb_dhe_[Zgbc\_dlhjZ?g_mihjy^hq_gghlZdhc ± g_iheyjbah\Zgguc ± k\_l gZau\Z_lky _kl_kl\_gguf Ijhkl_crbf ijbf_jhf iheyjbaZpbb y\ey_lky ijhoh`^_gb_ mijm]bo ihi_j_qguo \heg dhe_[Zgbc \_jz\db beb kljmguq_j_amadmxs_ev<u^_eyxl weebilbq_kdmx iheyjbaZpbx \hegu dhg_p \_dlhjZ ? hibku\Z_l weebik \iehkdhklbi_ji_g^bdmeyjghcdgZijZ\e_gbxjZkijhkljZg_gby\hegub_zqZklgu_kemqZb±pbjdmeyjgmx iheyjbaZpbx weebik \ujh`^Z_lky \ djm] b ebg_cgmx iehkdmx iheyjbaZpbxweebik\ujh`^Z_lky\ijyfmx<ihke_^g_fkemqZ_iehkdhklvijhoh^ysZyq_j_a\_dlhj?bgZijZ\e_gb_jZkijhkljZg_gbyemqZgZau\Z_lkyiehkdhklvxiheyjbaZpbb.Dhebq_kl\_gghc oZjZdl_jbklbdhc iheyjbaZpbb \heg kem`bl kl_i_gv iheyjbaZpbb:I −IP = max min , ]^_Imax bImin – fZdkbfZevgZybfbgbfZevgZybgl_gkb\ghklbj_]bkljbjm_fu_I max + I minijb ih\hjhl_ j_]bkljbjmxs_]h ijb[hjZ \hdjm] hkb jZkijhkljZg_gby k\_lZ >ey _kl_kl\_ggh]hk\_lZJ ^eyiehkdh iheyjbah\Zggh]hJ = 1.2) Ih]ehs_gb_k\_lZ:Ih]ehs_gb_ ± y\e_gb_ mf_gvr_gby wg_j]bb \hegu ijhoh^ys_c q_j_a \_s_kl\h aZkqzl_zi_j_oh^Z\h\gmlj_ggxxwg_j]bx\_s_kl\ZKqblZyqlhkl_i_gvih]ehs_gbyg_aZdI\bkbl hl bgl_gkb\ghklb ijhoh^ys_c \hegu ihemqbf= κ dx, lh _klv I = I 0e −κ x , ]^_ x –IlhesbgZkehy\_s_kl\ZWlhkhhlghr_gb_gZau\Z_lkyaZdhghf;m]_jZEZf[_jlZDhwnnbpb_gl κ – gZlmjZevgucihdZaZl_evih]ehs_gbyaZ\bkbfhklv κhl λ – ki_dljih]ehs_gby\_s_kl\Z.?keb ih]ehsZxs__ \_s_kl\h jZkl\hj_gh \ g_ih]ehsZxs_f jZkl\hjbl_e_ lh ijb fZeuo dhgp_gljZpbyo \uihegy_lky aZdhg ;_jZ: κ = α0k ]^_ k ± dhgp_gljZpby jZkl\hjzggh]h\_s_kl\Z α0±dhwnnbpb_glg_aZ\bkysbchldhgp_gljZpbb<dhgp_gljbjh\ZgguojZkl\hjZoaZdhg;_jZg_\uihegy_lkybaaZ\aZbfh^_ckl\byf_`^mih]ehsZxsbfbqZklbpZfbKh\hdmighklv ^Zgguo khhlghr_gbc gZau\Zxl aZdhghf ;m]_jZEZf[_jlZ;_jZ ijb gZebqbb g_ lhevdh ih]ehs_gby gh b jZkk_ygby kf g_h[oh^bfh \\_^_gb_ ihijZ\db gZ'wdklbgdpbxjZkk_ygb_κ’: I = I 0 e −(κ −κ )x .3) IheyjbaZpby\hegijbba[bjZl_evghfih]ehs_gbb:?keb\kbemhkh[_gghkl_ckljh_gby\_s_kl\hkbevg__ih]ehsZ_lk\_l\h^gbogZijZ\e_gbyobkeZ[__±\^jm]boZgbahljhibyih]ehs_gbylhijhbkoh^blqZklbqgZyiheyjbaZpbyk\_lZgZijZ\e_gb_iheyjbaZpbbkhhl\_lkl\m_lgZijZ\e_gbxgZbf_gvr_]hih]ehs_gbyIheyjbaZlhju (iheyjhb^u±\_s_kl\Zijbijhoh`^_gbbq_j_adhlhju_k\_lqZklbqghiheyjbam_lkyIjbf_jhfiheyjhb^h\y\eyxlky\_s_kl\Zba[bjZl_evghih]ehsZxsb_k\_l\dZdhfeb[h gZijZ\e_gbb – djbklZeeu lmjfZebgZ b iezgdbiheb\bgbeh\h]h kibjlZ beb ihebijhibe_gZIehkdhklv\dhlhjhciheyjbaZlhjemqr_ijhimkdZ_lk\_lgZau\Z_lky]eZ\ghciehkdhklvxiheyjhb^Z.Iheyjhb^ kqblZ_lky b^_Zevguf _keb hg iheghklvx [_a ihl_jb wg_j]bb ijhimkdZ_lemqb\_dlhj?\dhlhjuodhe_[e_lky\]eZ\ghciehkdhklbbg_ijhimkdZ_lemqb\dhlhjuo\_dlhj?i_ji_g^bdmeyj_gdwlhciehkdhklbIhke_ijhoh`^_gbyiZjZee_evgh]himqdZ_kl_kl\_ggh]hk\_lZq_j_ab^_ZevguciheyjbaZlhjk\_lklZgh\blkyebg_cghiheyjbah\ZggufJ_Zevgu_iheyjbaZlhjug_y\eyxlkyb^_ZevgufbbgZ\uoh^_^ZxlebrvqZklbqghiheyjbah\Zgguck\_lIjbiZ^_gbbgZb^_ZevguciheyjbaZlhjiehkdhiheyjbah\Zggh]hk\_lZZfieblm^Zdhe_[Zgbc\_dlhjZ?ihke_ijhoh`^_gbyq_j_aiheyjhb^ E = E0 cos ϕ , ]^_?0±Zfieblm^Z dhe_[Zgbc ^h ijhoh`^_gby ϕ ± m]he f_`^m iehkdhklvx iheyjbaZpbb k\_lZ b ]eZ\ghc32iehkdhklvxiheyjhb^ZLh]^Z I = I 0 cos 2 ϕ – aZdhgFZexkZ\uihegy_lkylhevdh^eyb^_ZevguoiheyjbaZlhjh\Iheyjhb^ubkihevam_lg_lhevdh^eyiheyjbaZpbb_kl_kl\_ggh]hk\_lZghb^eyZgZebaZk\_lZiheyjbah\Zggh]hgZijbf_j^eyhij_^_e_gbykl_i_gbiheyjbaZpbb<wlhfkemqZ_bogZau\ZxlZgZebaZlhjZfb.

AZdhghf_jghklb baemq_gby ^bihey IheyjbaZpby k\_lZijb hljZ`_gbb hl ih\_joghklb ^bwe_dljbdZ M]he ;jxkl_jZ IheyjbaZpby jZkk_yggh]h k\_lZ JZkk_ygb_fmlgufbkj_^Zfbbfhe_dmeyjgh_jZkk_ygb_AZdhgJwe_yIj_^klZ\e_gb_hjZkk_ygbbFb1) Baemq_gb_^bihey:Dhe_[Zgby we_dljhgh\ \ ZlhfZo m^h[gh ij_^klZ\eylv dZd dhe_[Zgby ^bihe_c y^jh ±g_ih^\b`guciheh`bl_evgucaZjy^Zwe_dljhgui_j_f_sZxlky\hdjm]y^jZ<ijhkl_cr_fkemqZ_hljbpZl_evgucaZjy^^\b`_lky\^hevh^ghcijyfhclZdqlh^bihevgucfhf_glbaf_JG JJGgy_lky ih ]Zjfhgbq_kdhfm aZdhgm p = p0 cos ω t. Lh]^Z baemq_gb_ ^bihey _klv baemq_gb_^\b`ms_]hkyaZjy^Z.<kydbc ^\b`msbcky aZjy^ fh`gh kqblZlv we_f_glhf lhdZ ijb wlhf i = ξ . Ih aZdhgmJG µµJJG G0 ;bhKZ\ZjZEZieZkZ fZ]gblgZy bg^mdpby \hagbdZxs_]h ihey d B =idl , r  ; \_dlhj <3 4π rJGJJGG .

.baf_gy_lky ih aZdhgm B (t ) ~  p0 r  ξ ~ ξ sin θ , ]^_ θ ± m]he f_`^m gZijZ\e_gb_f ^\b`_gbyaZjy^Z b gZijZ\e_gb_f gZ lhqdm gZ[ex^_gby.. 2dB ..E~~ ξ sin θ ⇒ I ~ ξ sin 2 θ ~ ω 4 sin 2 θ . LZdbf h[jZahfdt^bihev baemqZ_l fZdkbfZevgmx wg_j]bx \ gZijZ\e_gbyoi_ji_g^bdmeyjguo d k\h_c hkb b g_ baemqZ_l \^hev hkbIjhkljZgkl\_ggZy dZjlbgZ gZau\Z_lky ^bZ]jZffhc gZijZ\e_gghklb baemq_gby ^bihey fh`_l [ulv ihemq_gZ \jZs_gb_f iehkdhc dZjlbgu ij_^klZ\e_gghcgZjbkmgd_bij_^klZ\ey_lkh[hc^_nhjfbjh\Zgguclhjhb^Ba aZdhgZ ;bhKZ\ZjZEZieZkZ ke_^m_l qlh \_dlhj < i_ji_g^bdmeyj_g d iehkdhklbijhoh^ys_cq_j_ahkv^biheybgZijZ\e_gb_gZlhqdmgZ[ex^_gbywlhhagZqZ_lqlhbaemq_gb_ ^bihey iehkdhiheyjbah\Zgghijbqzf iehkdhklviheyjbaZpbb ± iehkdhklv ijhoh^ysZyq_j_ahkv^biheybgZijZ\e_gb_baemqZ_fuo\heg2) IheyjbaZpbyk\_lZijbhljZ`_gbb:IehkdhklviZ^_gby±iehkdhklvijhoh^ysZyq_j_aiZ^Zxsbcemqb ghjfZev d ih\_joghklb \ lhqd_ iZ^_gby ?keb emq iehkdhklv iheyjbaZpbb dhlhjh]h kh\iZ^Z_l k iehkdhklvxiZ^_gbyiZ^Z_lgZ]jZgbpmjZa^_eZ^\mo^bwe_dljbq_kdbonZalh\h\lhjhcnZa_\ha[m`^Zxlkydhe_[Zgby^bihe_ckh\iZ^Zxsb_ihgZijZ\e_gbxkhkvxdhe_[Zgbc\_dlhjZ?HljZ`zggmx b ij_ehfezggmx \hegu fh`gh kqblZlv j_amevlZlhf bgl_jn_j_gpbb \heg baemqZ_fuodhe_[exsbfbky^biheyfbIhaZdhgZf]_hf_ljbq_kdhchilbdbm]heiZ^_gbyjZ\_gm]emhljZ`_gbyh^gZdhijbhij_^_ezgghfm]e_iZ^_gbygZijZ\e_gb_hljZ`zggh]hemqZhdZ`_lkyi_ji_g^bdmeyjguf d gZijZ\e_gbx dhe_[Zgbc ^bihey Ihwlhfm hljZ`_gb_ ijhbkoh^blv g_[m^_lLZdhcm]hegZau\Z_lkym]ehf;jxkl_jZ α;.Imklv β; ± m]he ij_ehfe_gby khhl\_lkl\mxsbc m]em ;jxkl_jZ lh]^Z ba aZdhgZ ij_sin α ; n2πehfe_gby= , Z ba mkeh\by hlkmlkl\by hljZ`_gby α ; + β ; = ⇒ sin β ; = cos α ; ;sin β ; n1233n2.

Y\e_gb_ hlkmlkl\by hljZ`_gby ijb iZ^_gbb iehkdhiheyjbah\Zggh]h k\_lZ ih^n1m]ehf;jxkl_jZbkihevam_lky\eZa_jZo±ijbfgh]hdjZlghfijhoh`^_gbbemqZq_j_aljm[dmk Zdlb\guf \_s_kl\hf lj_[m_lky hlkmlkl\b_ hljZ`_gby gZ ih\_joghklb ljm[db ^ey wlh]hhdgZq_j_adhlhju_ijhoh^ylemqbjZkiheZ]Zxlihhlghr_gbxdgbfgZdehggh±ih^m]ehf;jxkl_jZ?keb iehkdhklv iZ^_gby i_ji_g^bdmeyjgZ d iehkdhklb iheyjbaZpbb lh ^biheb lZd`_[m^mldhe_[Zlvky\wlhciehkdhklb±ijhbahc^zlbgl_jn_j_gpbybaemqZ_fuo\hegkh[jZah\Zgb_f hljZ`zggh]h b ij_ehfezggh]h emq_c ± gb lhlgb^jm]hc g_ hdZ`_lky ih]Zr_ggufgh h[Z [m^ml iheyjbah\Zgu lZd`_ dZd b iZ^Zxsbc imqhd LZdbf h[jZahf ijb iZ^_gbb gZ]jZgbpmjZa^_eZnZa_kl_kl\_ggh]hk\_lZih^m]ehf;jxkl_jZijhbkoh^bliheyjbaZpbyhljZ`zggh]hk\_lZ\iehkdhklbi_ji_g^bdmeyjghcdiehkdhklbiZ^_gbybqZklbqgZyiheyjbaZpbyij_ehfezgguoemq_ctg α ; =3) JZkk_ygb_k\_lZ:JZkk_ygb_ k\_lZ ± ij_h[jZah\Zgb_ k\_lZ \_s_kl\hf khijh\h`^Zxs__ky baf_g_gb_fgZijZ\e_gbyb\hafh`ghqZklhluk\_lZijhy\eyxs__kydZdg_kh[kl\_ggh_k\_q_gb_\_s_kl\Z JZkk_ygb_ ± j_amevlZl bgl_jn_j_gpbb \heg baemqZ_fuo dhe_[exsbfbky ^biheyfbihwlhfmjZkk_ygb_gZ[ex^Z_lkyg_\h\k_okemqZyo<^hklZlhqghiehlghcjZkklhygb_f_`^mkhk_^gbfbqZklbpZfbfgh]hf_gvr_^ebgu\heguhilbq_kdbh^ghjh^ghckj_^_dZ`^hfmbaemqZl_exkhhl\_lkl\m_l^jm]hc±hlklhysbchli_j\h]hgZ λ/2.

Khhl\_lkl\_gghwlb^biheb ©]Zkylª ^jm] ^jm]Z ± jZkk_ygb_ g_ ijhbkoh^bl >ey gZ[ex^_gby jZkk_ygby g_h[oh^bfueb[hg_h^ghjh^gZyeb[hkbevghjZaj_`_ggZykj_^Z<i_j\hfkemqZ_gZ[ex^Z_lkyjZkk_ygb_fmlgufbkj_^Zfb\h\lhjhf±fhe_dmeyjgh_jZkk_ygb_.IjbihiZ^ZgbbemqZ_kl_kl\_ggh]hk\_lZgZjZkk_b\Zxsmx kj_^m\ha[m`^Zxlkydhe_[Zgby ^bihe_c baaZ g_iheyjbah\Zgghklb bkoh^gh]h imqdZ ^biheb dhe_[exlky \^hev \k_ogZijZ\e_gbce_`Zsbo\iehkdhklbi_ji_g^bdmeyjghcdgZijZ\e_gbxjZkijhkljZg_gbyemqZ Baemq_gby ^bihe_c dhe_[exsboky \^hev iZjZee_evguo ijyfuo iehkdh iheyjbah\ZguihwlhfmjZkk_ygguck\_l[m^_lqZklbqghiheyjbah\ZgZjZkk_yggucih^m]ehfπ/2d\_dlhjmkdhjhklb±iehkdhiheyjbah\ZgIjbiZ^_gbbgZjZkk_b\Zxsmxkj_^miehkdhiheyjbah\Zggh]hemqZ\k_^biheb\_s_kl\Z[m^mldhe_[Zlvky\^hevh^gh]hgZijZ\e_gbyihwlhfmjZkk_ygguck\_l[m^_llZd`_iehkdhiheyjbah\ZgIjbfhe_dmeyjghfjZkk_ygbbj_amevlbjmxsbcemqfh`ghjZkkfZljb\ZlvdZdj_amevlZlbgl_jn_j_gpbbbaemq_gbc ^bihe_cihwlhfm I j ~ ω 4 ~ λ −4 – aZdhg Jwe_y.

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