From e57f9b6f9ecb90556c314815b6c1afe4db7dc8cf Mon Sep 17 00:00:00 2001 From: Andrew Lorimer Date: Mon, 16 Jul 2018 15:43:13 +1000 Subject: [PATCH] add midyear cheatsheet, add ch8-9 notes for waves --- physics/midyear.aux | 1 + physics/midyear.fdb_latexmk | 29 +++- physics/midyear.fls | 45 +++-- physics/midyear.log | 319 ++++++++++++++++++------------------ physics/midyear.pdf | Bin 182369 -> 330962 bytes physics/midyear.synctex.gz | Bin 11230 -> 28411 bytes physics/midyear.tex | 187 ++++++++++++++++++++- physics/waves.md | 118 ++++++++++++- 8 files changed, 512 insertions(+), 187 deletions(-) diff --git a/physics/midyear.aux b/physics/midyear.aux index 0ed01dd..894cdc5 100644 --- a/physics/midyear.aux +++ b/physics/midyear.aux @@ -1,3 +1,4 @@ \relax \@writefile{toc}{\contentsline {section}{\numberline {1}Motion}{}} \@writefile{toc}{\contentsline {section}{\numberline {2}Relativity}{}} +\@writefile{toc}{\contentsline {section}{\numberline {3}Fields and power}{}} diff --git a/physics/midyear.fdb_latexmk b/physics/midyear.fdb_latexmk index 520331f..3b95bb6 100644 --- a/physics/midyear.fdb_latexmk +++ b/physics/midyear.fdb_latexmk @@ -1,13 +1,25 @@ # Fdb version 3 -["pdflatex"] 1531051766 "midyear.tex" "midyear.pdf" "midyear" 1531051767 +["pdflatex"] 1531545115 "midyear.tex" "midyear.pdf" "midyear" 1531545116 + "/mnt/andrew/graphics/ac-generator.png" 1529320281 28991 f74a831edcaed66632e709a6b2e2ebfd "" + "/mnt/andrew/graphics/ac-motor.png" 1529313736 18626 d0f4943be26fdce44a4ce45ccb01633c "" "/mnt/andrew/graphics/banked-track.png" 1531025364 51228 cc5d8f3f8efb06a64aca4afabfd63eed "" "/mnt/andrew/graphics/circ-forces.png" 1531025828 17259 bc7cee5c5abcaea13025f490d4a700af "" + "/mnt/andrew/graphics/dc-motor-2.png" 1529320688 53769 fc78422983cc0333d421ae3c4a8e8e14 "" + "/mnt/andrew/graphics/field-lines.png" 1529318258 13526 3230dbcdb592145e128b7e3f27f400ba "" "/mnt/andrew/graphics/projectile-motion.png" 1531026367 53128 73ac7f2c98d2d1322c2b7390ef77f5ea "" 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"/usr/share/texmf-dist/fonts/tfm/public/cm/cmbx10.tfm" 1525040101 1328 c834bbb027764024c09d3d2bf908b5f0 "" "/usr/share/texmf-dist/fonts/tfm/public/cm/cmbx12.tfm" 1525040101 1324 c910af8c371558dc20f2d7822f66fe64 "" "/usr/share/texmf-dist/fonts/tfm/public/cm/cmr12.tfm" 1525040101 1288 655e228510b4c2a1abe905c368440826 "" "/usr/share/texmf-dist/fonts/tfm/public/cm/cmr17.tfm" 1525040101 1292 296a67155bdbfc32aa9c636f21e91433 "" + "/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb" 1525040095 34811 78b52f49e893bcba91bd7581cdc144c0 "" "/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb" 1525040095 32080 340ef9bf63678554ee606688e7b5339d "" "/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmex10.pfb" 1525040095 30251 6afa5cb1d0204815a708a080681d4674 "" "/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb" 1525040095 36299 5f9df58c2139e7edcf37c8fca4bd384d "" @@ -18,17 +30,20 @@ "/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb" 1525040095 32762 224316ccc9ad3ca0423a14971cfa7fc1 "" "/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb" 1525040095 32569 5e5ddc8df908dea60932f3c484a54c0d "" "/usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb" 1525040095 32716 08e384dc442464e7285e891af9f45947 "" + "/usr/share/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb" 1525040095 31764 459c573c03a4949a528c2cc7f557e217 "" "/usr/share/texmf-dist/tex/context/base/mkii/supp-pdf.mkii" 1525040113 71627 94eb9990bed73c364d7f53f960cc8c5b "" - "/usr/share/texmf-dist/tex/generic/ifxetex/ifxetex.sty" 1525040105 1458 43ab4710dc82f3edeabecd0d099626b2 "" "/usr/share/texmf-dist/tex/generic/oberdiek/etexcmds.sty" 1525040105 7612 729a8cc22a1ee0029997c7f74717ae05 "" "/usr/share/texmf-dist/tex/generic/oberdiek/ifluatex.sty" 1525040105 7324 2310d1247db0114eb4726807c8837a0e "" "/usr/share/texmf-dist/tex/generic/oberdiek/ifpdf.sty" 1525040105 1251 d170e11a3246c3392bc7f59595af42cb "" - "/usr/share/texmf-dist/tex/generic/oberdiek/ifvtex.sty" 1525040105 6797 90b7f83b0ad46826bc16058b1e3d48df "" "/usr/share/texmf-dist/tex/generic/oberdiek/infwarerr.sty" 1525040105 8253 473e0e41f9adadb1977e8631b8f72ea6 "" "/usr/share/texmf-dist/tex/generic/oberdiek/kvdefinekeys.sty" 1525040105 5152 b67a3a964ad9851e095110c854a1d461 "" "/usr/share/texmf-dist/tex/generic/oberdiek/kvsetkeys.sty" 1525040105 14040 ac8866aac45982ac84021584b0abb252 "" "/usr/share/texmf-dist/tex/generic/oberdiek/ltxcmds.sty" 1525040105 18425 5b3c0c59d76fac78978b5558e83c1f36 "" "/usr/share/texmf-dist/tex/generic/oberdiek/pdftexcmds.sty" 1525040105 20418 ca44694be1c8df491925faa194fe6edf "" + "/usr/share/texmf-dist/tex/latex/amsfonts/amsfonts.sty" 1525040104 5949 3f3fd50a8cc94c3d4cbf4fc66cd3df1c "" + "/usr/share/texmf-dist/tex/latex/amsfonts/amssymb.sty" 1525040104 13829 94730e64147574077f8ecfea9bb69af4 "" + "/usr/share/texmf-dist/tex/latex/amsfonts/umsa.fd" 1525040104 961 6518c6525a34feb5e8250ffa91731cff "" + "/usr/share/texmf-dist/tex/latex/amsfonts/umsb.fd" 1525040104 961 d02606146ba5601b5645f987c92e6193 "" "/usr/share/texmf-dist/tex/latex/amsmath/amsbsy.sty" 1525040104 2211 ca7ce284ab93c8eecdc6029dc5ccbd73 "" "/usr/share/texmf-dist/tex/latex/amsmath/amsgen.sty" 1525040104 4161 7f6eb9092061a11f87d08ed13515b48d "" "/usr/share/texmf-dist/tex/latex/amsmath/amsmath.sty" 1525040104 84354 7292177bb735c466b78634ee4efd537e "" @@ -37,7 +52,7 @@ "/usr/share/texmf-dist/tex/latex/base/article.cls" 1525040104 19823 fcbc01552b07b608574cbf8e1977e0c0 "" "/usr/share/texmf-dist/tex/latex/base/omscmr.fd" 1525040104 2472 aa08940f0a4dc6c24ae9f943b04ae0b9 "" "/usr/share/texmf-dist/tex/latex/base/size10.clo" 1525040104 8294 b0f177401f895563eb19304d2389582d "" - "/usr/share/texmf-dist/tex/latex/geometry/geometry.sty" 1525040104 41366 3ed245b911039f45436c2cb62a4d1e62 "" + "/usr/share/texmf-dist/tex/latex/enumitem/enumitem.sty" 1525020838 42666 6fa770e3485520a6a5f2ea7d259c8f8d "" "/usr/share/texmf-dist/tex/latex/graphics-cfg/graphics.cfg" 1525040104 1224 978390e9c2234eab29404bc21b268d1e "" "/usr/share/texmf-dist/tex/latex/graphics-def/pdftex.def" 1525040104 17334 520b9b85ad8a2a48eda3f643e27a5179 "" "/usr/share/texmf-dist/tex/latex/graphics/graphics.sty" 1525040104 15272 5a97061616e0c8b2aa79c6615ff769f4 "" @@ -55,9 +70,9 @@ "/usr/share/texmf-dist/web2c/texmf.cnf" 1525040116 33301 a3134070eacafb10b1f371612ce2650d "" "/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map" 1530607795 2586890 ddabbb88c498d59d5daa7919afb0a27f "" "/var/lib/texmf/web2c/pdftex/pdflatex.fmt" 1530607774 7906415 c2bc2a1e85cbebe301ae391211242f7e "" - "midyear.aux" 1531051767 146 a59c3471c01dfdc38f374ef57c657d3c "" - "midyear.tex" 1531051765 2909 a6a51cef65d7d592a8a6d071f6f9bbf7 "" + "midyear.aux" 1531545115 223 c9c8cc73e6c5d1c4bae220d8eb29b53c "" + "midyear.tex" 1531545115 7760 df61705a0ad9f9a0549b9ac5cd9a1da8 "" (generated) "midyear.aux" - "midyear.log" "midyear.pdf" + "midyear.log" diff --git a/physics/midyear.fls b/physics/midyear.fls index a8fd227..fd1ed4e 100644 --- a/physics/midyear.fls +++ b/physics/midyear.fls @@ -7,16 +7,6 @@ INPUT /usr/share/texmf-dist/tex/latex/base/article.cls INPUT /usr/share/texmf-dist/tex/latex/base/article.cls INPUT /usr/share/texmf-dist/tex/latex/base/size10.clo INPUT /usr/share/texmf-dist/tex/latex/base/size10.clo -INPUT /usr/share/texmf-dist/tex/latex/geometry/geometry.sty -INPUT /usr/share/texmf-dist/tex/latex/geometry/geometry.sty -INPUT /usr/share/texmf-dist/tex/latex/graphics/keyval.sty -INPUT /usr/share/texmf-dist/tex/latex/graphics/keyval.sty -INPUT /usr/share/texmf-dist/tex/generic/oberdiek/ifpdf.sty -INPUT /usr/share/texmf-dist/tex/generic/oberdiek/ifpdf.sty -INPUT /usr/share/texmf-dist/tex/generic/oberdiek/ifvtex.sty -INPUT /usr/share/texmf-dist/tex/generic/oberdiek/ifvtex.sty -INPUT /usr/share/texmf-dist/tex/generic/ifxetex/ifxetex.sty -INPUT /usr/share/texmf-dist/tex/generic/ifxetex/ifxetex.sty INPUT /usr/share/texmf-dist/tex/latex/tools/multicol.sty INPUT /usr/share/texmf-dist/tex/latex/tools/multicol.sty INPUT /usr/share/texmf-dist/tex/latex/preprint/fullpage.sty @@ -31,10 +21,16 @@ INPUT /usr/share/texmf-dist/tex/latex/amsmath/amsbsy.sty INPUT /usr/share/texmf-dist/tex/latex/amsmath/amsbsy.sty INPUT /usr/share/texmf-dist/tex/latex/amsmath/amsopn.sty INPUT /usr/share/texmf-dist/tex/latex/amsmath/amsopn.sty +INPUT /usr/share/texmf-dist/tex/latex/amsfonts/amssymb.sty +INPUT /usr/share/texmf-dist/tex/latex/amsfonts/amssymb.sty +INPUT /usr/share/texmf-dist/tex/latex/amsfonts/amsfonts.sty +INPUT /usr/share/texmf-dist/tex/latex/amsfonts/amsfonts.sty INPUT /usr/share/texmf-dist/tex/latex/setspace/setspace.sty INPUT /usr/share/texmf-dist/tex/latex/setspace/setspace.sty INPUT /usr/share/texmf-dist/tex/latex/graphics/graphicx.sty INPUT /usr/share/texmf-dist/tex/latex/graphics/graphicx.sty +INPUT /usr/share/texmf-dist/tex/latex/graphics/keyval.sty +INPUT /usr/share/texmf-dist/tex/latex/graphics/keyval.sty INPUT /usr/share/texmf-dist/tex/latex/graphics/graphics.sty INPUT /usr/share/texmf-dist/tex/latex/graphics/graphics.sty INPUT /usr/share/texmf-dist/tex/latex/graphics/trig.sty @@ -45,6 +41,8 @@ INPUT /usr/share/texmf-dist/tex/latex/graphics-def/pdftex.def INPUT /usr/share/texmf-dist/tex/latex/graphics-def/pdftex.def INPUT /usr/share/texmf-dist/tex/latex/wrapfig/wrapfig.sty INPUT /usr/share/texmf-dist/tex/latex/wrapfig/wrapfig.sty +INPUT /usr/share/texmf-dist/tex/latex/enumitem/enumitem.sty +INPUT /usr/share/texmf-dist/tex/latex/enumitem/enumitem.sty INPUT midyear.aux INPUT midyear.aux OUTPUT midyear.aux @@ -70,6 +68,8 @@ INPUT /usr/share/texmf-dist/tex/generic/oberdiek/ifluatex.sty INPUT /usr/share/texmf-dist/tex/generic/oberdiek/ifluatex.sty INPUT /usr/share/texmf-dist/tex/generic/oberdiek/pdftexcmds.sty INPUT /usr/share/texmf-dist/tex/generic/oberdiek/pdftexcmds.sty +INPUT /usr/share/texmf-dist/tex/generic/oberdiek/ifpdf.sty +INPUT /usr/share/texmf-dist/tex/generic/oberdiek/ifpdf.sty INPUT /usr/share/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg INPUT /usr/share/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg INPUT /usr/share/texmf-dist/fonts/map/fontname/texfonts.map @@ -80,6 +80,16 @@ INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmr12.tfm INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmbx12.tfm INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm +INPUT /usr/share/texmf-dist/tex/latex/amsfonts/umsa.fd +INPUT /usr/share/texmf-dist/tex/latex/amsfonts/umsa.fd +INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam10.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam7.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam5.tfm +INPUT /usr/share/texmf-dist/tex/latex/amsfonts/umsb.fd +INPUT /usr/share/texmf-dist/tex/latex/amsfonts/umsb.fd +INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm +INPUT /usr/share/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm5.tfm INPUT /mnt/andrew/graphics/banked-track.png INPUT /mnt/andrew/graphics/banked-track.png OUTPUT midyear.pdf @@ -92,8 +102,22 @@ INPUT /usr/share/texmf-dist/tex/latex/base/omscmr.fd INPUT /mnt/andrew/graphics/projectile-motion.png INPUT /mnt/andrew/graphics/projectile-motion.png INPUT /mnt/andrew/graphics/projectile-motion.png +INPUT /usr/share/texmf-dist/fonts/tfm/public/cm/cmbx10.tfm INPUT /var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map +INPUT /mnt/andrew/graphics/field-lines.png +INPUT /mnt/andrew/graphics/field-lines.png +INPUT /mnt/andrew/graphics/field-lines.png +INPUT /mnt/andrew/graphics/ac-generator.png +INPUT /mnt/andrew/graphics/ac-generator.png +INPUT /mnt/andrew/graphics/ac-generator.png +INPUT /mnt/andrew/graphics/dc-motor-2.png +INPUT /mnt/andrew/graphics/dc-motor-2.png +INPUT /mnt/andrew/graphics/dc-motor-2.png +INPUT /mnt/andrew/graphics/ac-motor.png +INPUT /mnt/andrew/graphics/ac-motor.png +INPUT /mnt/andrew/graphics/ac-motor.png INPUT midyear.aux +INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmex10.pfb INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb @@ -104,3 +128,4 @@ INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr5.pfb INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb +INPUT /usr/share/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb diff --git a/physics/midyear.log b/physics/midyear.log index 02e6a27..8d34683 100644 --- a/physics/midyear.log +++ b/physics/midyear.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2018/Arch Linux) (preloaded format=pdflatex 2018.7.3) 8 JUL 2018 22:09 +This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2018/Arch Linux) (preloaded format=pdflatex 2018.7.3) 14 JUL 2018 15:11 entering extended mode restricted \write18 enabled. file:line:error style messages enabled. @@ -23,50 +23,25 @@ File: size10.clo 2014/09/29 v1.4h Standard LaTeX file (size option) \abovecaptionskip=\skip41 \belowcaptionskip=\skip42 \bibindent=\dimen102 -) (/usr/share/texmf-dist/tex/latex/geometry/geometry.sty -Package: geometry 2018/03/24 v5.7 Page Geometry - (/usr/share/texmf-dist/tex/latex/graphics/keyval.sty -Package: keyval 2014/10/28 v1.15 key=value parser (DPC) -\KV@toks@=\toks14 -) (/usr/share/texmf-dist/tex/generic/oberdiek/ifpdf.sty -Package: ifpdf 2017/03/15 v3.2 Provides the ifpdf switch -) (/usr/share/texmf-dist/tex/generic/oberdiek/ifvtex.sty -Package: ifvtex 2016/05/16 v1.6 Detect VTeX and its facilities (HO) -Package ifvtex Info: VTeX not detected. -) (/usr/share/texmf-dist/tex/generic/ifxetex/ifxetex.sty -Package: ifxetex 2010/09/12 v0.6 Provides ifxetex conditional -) -\Gm@cnth=\count88 -\Gm@cntv=\count89 -\c@Gm@tempcnt=\count90 -\Gm@bindingoffset=\dimen103 -\Gm@wd@mp=\dimen104 -\Gm@odd@mp=\dimen105 -\Gm@even@mp=\dimen106 -\Gm@layoutwidth=\dimen107 -\Gm@layoutheight=\dimen108 -\Gm@layouthoffset=\dimen109 -\Gm@layoutvoffset=\dimen110 -\Gm@dimlist=\toks15 ) (/usr/share/texmf-dist/tex/latex/tools/multicol.sty Package: multicol 2018/04/01 v1.8r multicolumn formatting (FMi) -\c@tracingmulticols=\count91 +\c@tracingmulticols=\count88 \mult@box=\box26 -\multicol@leftmargin=\dimen111 -\c@unbalance=\count92 -\c@collectmore=\count93 -\doublecol@number=\count94 -\multicoltolerance=\count95 -\multicolpretolerance=\count96 -\full@width=\dimen112 -\page@free=\dimen113 -\premulticols=\dimen114 -\postmulticols=\dimen115 +\multicol@leftmargin=\dimen103 +\c@unbalance=\count89 +\c@collectmore=\count90 +\doublecol@number=\count91 +\multicoltolerance=\count92 +\multicolpretolerance=\count93 +\full@width=\dimen104 +\page@free=\dimen105 +\premulticols=\dimen106 +\postmulticols=\dimen107 \multicolsep=\skip43 \multicolbaselineskip=\skip44 \partial@page=\box27 \last@line=\box28 -\maxbalancingoverflow=\dimen116 +\maxbalancingoverflow=\dimen108 \mult@rightbox=\box29 \mult@grightbox=\box30 \mult@gfirstbox=\box31 @@ -88,14 +63,14 @@ Package: multicol 2018/04/01 v1.8r multicolumn formatting (FMi) \@tempa=\box47 \@tempa=\box48 \@tempa=\box49 -\c@columnbadness=\count97 -\c@finalcolumnbadness=\count98 -\last@try=\dimen117 -\multicolovershoot=\dimen118 -\multicolundershoot=\dimen119 +\c@columnbadness=\count94 +\c@finalcolumnbadness=\count95 +\last@try=\dimen109 +\multicolovershoot=\dimen110 +\multicolundershoot=\dimen111 \mult@nat@firstbox=\box50 \colbreak@box=\box51 -\mc@col@check@num=\count99 +\mc@col@check@num=\count96 ) 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zYrX+Y_+8!j%=Gj0B$}i)m8=7SK%0=GaP#&NJ{j119r{_a{AcRh=)RczH%Y7S*_=c6 zyhhmT$i*>HI-hQTD(4&nj6(OYQ3W^kYDI{5m@p4 2.2 \operatorname{\mu s}$} + {\item slower time - more time to travel, so muons reach surface} +\end{itemize} + +\section{Fields and power} + + +\subsection*{Non-contact forces} +\begin{itemize} + {\item electric fields (dipoles \& monopoles)} + {\item magnetic fields (dipoles only)} + {\item gravitational fields (monopoles only)} +\end{itemize} + +\begin{itemize} +\item monopoles: field lines radiate towards central object +\item dipoles - field lines $+ \rightarrow -$ or $\operatorname{N} \rightarrow \operatorname{S}$ (opposite in solenoid) +\item closer field lines means larger force +\item dot means out of page, cross means into page +\end{itemize} + +\subsection*{Gravity} +\[ +F_g=G{{m_1m_2}\over r^2}\tag{grav. force} +\] + +\[ +g={F_g \over m}=G{M_{\operatorname{planet}} \over r^2}\tag{grav. acc.} +\] + +\[ +E_g = mg \Delta h\tag{gpe} +\] + +\[ +W = \Delta E_g = Fx\tag{work} +\] + +\subsection*{Satellites} +\[ +v=\sqrt{GM \over r} = \sqrt{gr} = {{2 \pi r} \over T} +\] + +\[ +T={\sqrt{4 \pi^2 r^2} \over {GM}}\tag{period} +\] + +\[ +\sqrt[3]{{GMT^2}\over{4\pi^2}}\tag{radius} +\] + + + +\subsection*{Magnetic fields} +% \begin{itemize} +% \item field strength $B$ measured in tesla +% \item magnetic flux $\Phi$ measured in weber +% \item charge $q$ measured in coulombs +% \item emf $\mathcal{E}$ measured in volts +% \end{itemize} + +% \[ +% {E_1 \over E_2}={r_1 \over r_2}^2 +% \] + +\[ +F=qvB\tag{force on moving charged particles} +\] + +if $B {\not \perp} A, \Phi \rightarrow 0$ \hspace{1em}, \hspace{1em} if $B \parallel A, \Phi = 0$ + + +\includegraphics[height=2cm]{/mnt/andrew/graphics/field-lines.png} + +\subsection*{Electric fields} + +\begin{align*} +F=qE \tag{$E$ = strength} \\ +W=q_{\operatorname{point}}\Delta V \tag{in field or points} \\ +F=k{{q_1q_2}\over r^2}\tag{force between $q_{1,2}$} \\ +E=k{Q \over r^2} \tag{$r=||EQ||$} \\ +F=BInl \tag{force on a coil} \\ +\Phi = B_{\perp}A\tag{magnetic flux} \\ +\mathcal{E} = -N{{\Delta \Phi}\over{\Delta t}} \tag{induced emf} \\ +{V_p \over V_s}={N_p \over N_s}={I_s \over I_p} \tag{xfmr coil ratios} \\ +\end{align*} + + +\textbf{Lenz's law:} ``$-n$'' in Faraday - emf opposes $\Delta \Phi$ + +\textbf{Eddy currents:} counter movement within a field + +\textbf{Right hand grip:} thumb points to north or $I$ + +\textbf{Right hand slap:} field, current, force are $\perp$ + +\textbf{Flux-time graphs:} gradient $\times n = \operatorname{emf}$ + +\textbf{Transformers:} core strengthens \& focuses $\Phi$ + +% \columnbreak + +\subsection*{Power transmission} + +\begin{align*} + V_{\operatorname{rms}}={V_{\operatorname{p\rightarrow p}}\over \sqrt{2}} \tag + P_{\operatorname{loss}} = \Delta V I = I^2 R = {{\Delta V^2} \over R} +\end{align*} + +\begin{itemize} + {\item Parallel - voltage is constant} + {\item Series - voltage is shared within branch} +\end{itemize} + +\includegraphics[height=4cm]{/mnt/andrew/graphics/ac-generator.png} +\subsection*{Motors} +% \begin{wrapfigure}{r}{-0.1\textwidth} +\includegraphics[height=4cm]{/mnt/andrew/graphics/dc-motor-2.png} +\includegraphics[height=3cm]{/mnt/andrew/graphics/ac-motor.png} \\ +% \end{wrapfigure} +\textbf{DC:} split ring (one ring split into two halves) +% \begin{wrapfigure}{r}{0.3\textwidth} +% \end{wrapfigure} +\textbf{AC:} slip ring (separate rings with constant contact) \end{multicols} diff --git a/physics/waves.md b/physics/waves.md index 92cf75d..0b085c5 100644 --- a/physics/waves.md +++ b/physics/waves.md @@ -1,24 +1,124 @@ # Waves -## Longitudinal and Transverse Waves +## Mechanical waves +- need a medium to travel through +- cannot transfer energy through vacuum +- individual particles have little movement regardless of the distance of wave +- **transfer of energy without net transfer of matter** -Longitudinal - direction of motion parallel to wave -Transverse - direction of motion perpendicular to wave +**Nodes** - point of no motion (fixed point on graph) +**Antinodes** - point of maximum motion (peaks) +**Crests** (peaks) & **troughs** (azimuths) -## Wavelength & frequency +### Longitudinal waves +**Direction of motion is parallel to wave** -$$v=f \times \lambda$$ +![](/mnt/andrew/graphics/longitudinal-waves.png) + +### Transverse waves +**Direction of motion is perpendicular to wave** +- rarefactions (expansions) +- compressions +![](/mnt/andrew/graphics/transverse-waves.png) + +### Measuring mechanical waves + +**Amplitude $A$** - max displacement from rest position (0) +**Wavelength $\lambda$** - distance between two points of same y-value (points are in phase) +**Frequency $f$** - number of cycles (wavelengths) per second + +$T={1 \over f}\quad$(period: time for one cycle) +$v=f \lambda \quad$(speed: displacement per second) + +### Doppler effect +- occurs when there is relative movement between source and observer +- inverse relationship between frequency and distance: $f \propto {1 \over d}$ +- applies to all types of wave +- only affects apparent $f$; actual $f$ is constant + +When $P_1$ approaches $P_2$, each wave $w_n$ has slightly less distance to travel than $w_{n-1}. Hence, $w_n$ reaches the observer sooner than $w_{n-1}, increasing "apparent" wavelength. -Nodes - point of no motion -Antinodes - point of maximum motion (peaks) -Crests (peaks) & troughs (azimuths) ## Interference patterns -Standing wave - constructive interference at resonant frequency +When a medium changes character: +- some energy is *reflected* +- some energy is *absorbed* by new medium +- some energy is *transmitted* + +**Superposition** - stimuli add together at a given point (vector addition) +**Standing wave** - constructive interference at resonant frequency + +### Reflection + +**Diffuse** reflection - irregular surface reflects each ray in a different angle. + +#### Rays +Two- or three-dimensional *wave fronts* can be reflected, e.g. waves at a beach. + +Direction of motion of wave fronts can be shown by arrows, called *rays*, which are perpendicular to the wave front: + +![](/mnt/andrew/graphics/rays.png) + +Angle of incidence $\theta_i =$ angle of reflection $\theta_r$ +- Normal: $\perp$ to wall +- Incident wave front: $\perp$ to incident ray +- Incident ray: $ + +#### Transverse +- sign of reflected transverse wave is inverted when endpoint is fixed in y-axis (equivalent to $180^\circ=\pi={\lambda \over 2}$ phase change) +- phase is constant if endpoint is free to move in y-axis (**reflected** is same as **incident**) + +## Harmonics + +**Harmonic** - fundamental (lowest) frequency to produce a certain number of wavelengths +**Overtone** - a multiple of the fundamental harmonic which produces the same no. of wavelengths at a different frequency (due to constructive interference) + +#### Wave has antinodes at both ends: +$\lambda = {{2l} \div n}\quad$ (wavelength for $n^{th}$ harmonic) +$f = {nv \div 2l}\quad$ (frequency for $n_{th}$ harmonic at length $l$ and speed $v$) + +#### Wave has antinode at one end: +$\lambda = {{4l} \div n}\quad$ (wavelength for $n^{th}$ harmonic) +$f = {nv \div 4l}\quad$ (frequency for $n_{th}$ harmonic at length $l$ and speed $v$) + +## Light + +Newton - light as a particle +- light speeds up as it travels through a solid medium + +Hooke - light as a wave +- light slows down through solid medium + +### Huygen's principle +**Each point on a wavefront can be considered a source of secondary wavelets** +![](/mnt/andrew/graphics/huygen.png) + +### Refraction +**Change in direction caused by change in speed** e.g. prism +$\Delta v$ depends on $\lambda$, so wavelengths become "split" +![](/mnt/andrew/graphics/refraction.png) + +Refractive index of a medium depends $\Delta v$ from $c$ +$n={c \over v}\quad$ (refractive index of a medium) +$n_1v_1=n_2v_2$ (equivalence between media) + +### Snell's law +$n$ can be used to determine how much a ray will refract going between two media. + +$$n_1 \sin \theta_1=n_2 \sin \theta_2$$ + +### Total internal reflection +When $n_1 < n_2$, light is refracted *towards* normal ($90^\circ$ to medium border - "vertical" line in case of air/water). +When $n_1 > n_2$, light is reflected *away* from normal. +**Critical angle $\theta_c$** - angle of incidence $\theta_1$ at which $\theta_2 \gt 90^\circ$ to normal +$n_1 sin \theta_c = n_2 \sin 90^\circ$ +$\therefore \theta_c = {n_2 \over n_1}$ + +### Dispersion -- 2.43.2