Sound Waves 15 | HP 50g Graphing, 48gII Graphing instruction

Sound Waves (15, 3)

Equations:

v =	B	I =	1	⋅ ρ ⋅ v ⋅ ω 2 ⋅ sm2
	ρ		2
	 I 
β = 10 ⋅ LOG 10 				ω = 2 ⋅ π ⋅ f

Example:

Given: sm=10_cm, ω=6000_r/s, B=12500_kPa, ρ=65_kg/m^3.

Solution: v=438.5290_m/s, I=5130789412.97_W/m^2, β=217.018_dB, f=954.9297_Hz.

560 Equation Reference

Image 496

HP 50g Graphing, 48gII Graphing manual Sound Waves 15

Contents

HP 50g / 49g+ / 48gII graphing calculator Advanced user’s reference manualPage Acknowledgements Printing HistoryPage Contents Names AlgbAlog Amort 317 Delalarm Delay→COL COL→ 359 Findalarm EXP2POWExpan Expand Halt IBPIDIV2 Iferr List MAX MaxrMIN Not PA2B2 ParametricParity Parsurface 3183 RND RnrmRoll Rolld 3226 Tabvar →TAGTail TAN Wireframe UpdirUtpc Utpf Contents 514 →ALG Apeek ARM→ ASM ASM→ 610 Alrmdat CST Exited Expr Iopar MASD.INIToff Tpar Vpar Contents of a Program Understanding Programming Examples of Program Actions Calculations in a ProgramProgram Results To enter commands and other objects in a program Entering and Executing ProgramsTo enter a program To store or name a program To stop an executing program 3Q!Ì*4`3/*@Ï3Q!Ì*4#3/* @Ë@Ï @% @Ér # O4 /3 *!Ì Q3 @Ë@Ï Program Keys Comments LevelOsph K To switch between entry modes Viewing and Editing ProgramsTo view or edit a program @%SPH% ˜ Using Local Variables Creating Programs on a ComputerCreating Local Variables `J!%SPH% @%SPH% ˜ Program Comments `OSPHLV K Evaluating Local Names Defining the Scope of Local Variables Compiled Local Variables Creating UserDefined Functions as Programs Using Tests and Conditional Structures Testing ConditionsKey Programmable Description Command To include a test in a program Using Logical Functions Keys Programmable Description CommandLogical Functions TEST% L Using Conditional Structures and Commands To enter if then END in a programPress !%BRCH% !%IF% To enter IFT in a program To enter if then Else END in a program Press !%BRCH% @%#IF#%To enter Ifte in a program or in an algebraic Press !%BRCH% L!%IFTE% To enter Case END in a program Conditional Examples Otst K 26 `52 J %TST% Using Definite Loop Structures Using Loop StructuresWhile … Repeat … END Start Next Structure « … start finish Start loopclause Next … »To enter Start Next in a program Press !%BRCH% !%START% Start Step Structure « … start finish Start loopclause increment Step … »To enter Start Step in a program Press ! %BRCH% … %START% For Next Structure « … start finish for counter loopclause Next … »To enter for Next in a program Press !%BRCH% ! %FOR% For Step Structure « … start finish for counter loopclause increment Step … »To enter for Step in a program Press ! %BRCH% … %FOR% Using Indefinite Loop Structures Do Until END Structure« … do loopclause Until testclause END … » To enter do Until END in a program Duplicates n, stores the value into n While Repeat END Structure « … While testclause Repeat loopclause END … »To enter While Repeat END in a program Press !%BRCH% ! %WHILE% To enter Incr or Decr in a program Using Loop CountersPress ! #MEM# %ARITH% %INCR% or %DECR% Using Summations Instead of Loops ∑ j Using Flags Setting, Clearing, and Testing FlagsTypes of Flags To set, clear, or test a flag Recalling and Storing the Flag States ExampleMonth/day/year format Day.month.year format Using Subroutines To recall the current flag statesExecute Rclf !L %MODES% %FLAG% L%RCLF% To change the current flag states Torsv K Torsa K` 8 J %TORSV% To singlestep from the start of a program To turn off the Halt annunciator at any timePress !LL %RUN% %KILL% @·J6 `8 `O%TORSV% !LL%RUN% %DBUG% To singlestep from the middle of a program To singlestep when the next step is a subroutine@·J10 `12 O%TORSV% !LL%RUN% %DBUG% Trapping Errors Causing and Analyzing ErrorsTo cause a userdefined error to occur in a program SingleStep Operations To artificially cause a builtin error to occur in a program To analyze an error in a programError Trapping Commands %ERROR% Making an Error Trap « … Iferr trapclause then errorclause END … »Press !LL %ERROR% !%IFERR% Iferr then END Structure Iferr then Else END Structure Press !LL %ERROR% @%IFERR%To enter Iferr then Else END in a program Data Input Commands Using PROMPT, Cont for InputKey Command Description Input `OTPROMPT ‰ @·J %TPROM% To enter Disp Freeze Halt in a program Using Disp Freeze HALT, Cont for InputTo respond to Halt while running a program Using INPUT, Enter for Input « … promptstring commandline Input OBJ→ … »To enter Input in a program To respond to Input while running a program %VSPH% Commandline cursorposition operatingoptions To design the commandline string for InputTo include Input options Cursorposition Press @ Õ ! Ê a @ To process the result string from Input`O Tinput ‰ %TINPU% Using Inform and Choose for Input To set up an input form To set up a choose box `OPHONES ‰ Using Wait for Keystroke Input Beeping to Get AttentionTo enter Beep in a program To enter Wait in a program Using KEY for Keystroke Input Data Output CommandsOutput OUT% Labeling Output with Tags Labeling and Displaying Output as StringsTo label a result with a tag %TTAG% 1.5 ˜1.85 ` Pausing to Display Output Using Msgbox to Display OutputTo set up a message box `OTSTRING ‰ Using Menus with Programs Using Menus for Input Using Menus to Run Programs To create a menubased applicationOlst ‰ SI% @·J%EIZ% Turning Off the Calculator from a Program %% !Ü.37~@6 68 %%I%% !%%Z%%@%%I%% 2*%%I%% !%%E%% To turn off the calculator in a programPage FIB1 Fibonacci Numbers, Recursive Version Fibonacci NumbersRPL Programming Examples %FIB1% FIB2 Fibonacci Numbers, Loop VersionFIB1% !Ü10 N %FIB2% FIB2 program listing10 %FIB2% Fibt Comparing ProgramExecution Time Techniques used in FibtStructured programming. Fibt calls both FIB1 and FIB2 Required Programs Displaying a Binary Integer PAD Pad with Leading Spaces13 %FIBT% Techniques used in PAD Preserve Save and Restore Previous Status PAD program listing`OPAD K Techniques used in Preserve Preserve program listing Bdisp Binary Display`OPRESERVE K Techniques used in Bdisp PAD Bdisp program listing `OBDISP K Tile Percentile of a list Median of Statistics Data144 %BDISP% Median Median of Statistics Data Techniques used in %TILETile program listing `O%TILE K Techniques used in Median Required Program Expanding and Collecting Completely `OMEDIAN K18 `12 `˜šš 11 `1 ` Multi Multiple Execution Techniques used in MultiMulti program listing `OMULTI K Exco Expand and Collect Completely Techniques used in ExcoExco program listing `OEXCO K Minimum and Maximum Array Elements MNX Minimum or Maximum Element-VersionÜ4 *Y+Z + User and system flags for logic control MNX program listing `OMNX K 12 `56 `˜šš 45 `1 ` MNX2 Minimum or Maximum Element-VersionTechniques used in MNX2 MNX2 program listing Applying a Program to an Array %MNX2%Techniques used in Aply Aply program listing Make sure the flag 1 is clear to begin Converting Between Number Bases `OAPLY KÔ3†2W†4` ‚Å 3 QA *7 `J %APLY% H#DISP ˜˜ Techniques used in nBASE NBASE program listing Verifying Program Arguments 1000 `23 J %NBASE% Names Check List for Exactly Two Names Techniques used in NamesNames program listing `ONAMES K Techniques used in VFY VFY Verify Program ArgumentVFY program listing Converting Procedures from Algebraic to RPN Oben `Ojeff ` Osarah ` %LIST% %²LIST% Techniques used in →RPN →RPN program listing XQ3 `%²RPN% Bessel FunctionsTechniques used in BER BER program listing `OBER K%BER% %BER% !Ü2 Animation of Successive Taylor’s Polynomials Sintp Converting a Plot to a Graphics ObjectTechniques used in Sintp Sintp program listing Setts Superimposing Taylor’s polynomials Techniques used in SettsSetts program listing `OSETTS K TSA Animating Taylor’s Polynomials Techniques used in TSATSA program listing `OTSA K Programmatic use of matrices and statistics commands Programmatic Use of Statistics and PlottingTechniques used in PIE Temporary menu for data input Angle `OPIE K 983 %SLICE% 416 %SLICE% 85 %SLICE% Trace Mode Techniques used in αENTER and ßENTERΑENTER program listing ßENTER program listing InverseFunction Solver Techniques used in RootrRootr program listing `OROOTR K Animating a Graphical Image @Å@É x †O3.7%X²FX% ` 599.5 ` 1 %ROOTR% Techniques used in Walk `OWALK K Introduction AcosType Input/Output Other Provided Details How Commands Are AlphabetizedParallel Processing with Lists Computer Algebra System Commands and Functions Classification of Operations Backup identifier Realnumber time or angle in hoursminutessecond s formatLibrary identifier Binary integer ABS AbcuvACK Ackall Type Description ACOS2S ASIN, ATAN, COS, Isol Acosh ASIN2C, ASIN2T, ATAN2SAcosh z Symb ACOSHsymb ADD Addtmod Addtoreal AlgbAlog 10z Principal Interest Balance AmortTVM, TVMBEG, TVMEND, Tvmroot Animate ANS Apply Access …µAPPLY Input/OutputARC Archive ARG Access …µARRY→ Input/Output AritARRY→ →ARRY Access !¼ ¼is the leftshift of the Skey ASIN2T ASIN2CAsinh ASN Asinh zSymb ASINHsymb ACOSH, ATANH, ISOL, Sinh Access … ÃL BIT ASR ASRAssume Skey Atan ADDTOREAL, Unassume ATAN2S Atan zSymb ATANsymb ACOS, ASIN, ISOL, TAN Access …µATICK AtanhAtick Atanh z Access …µATTACH Input/Output AttachAugment #n #m Access …µAUTO Input/Output None AutoAxes BAR Access …µAXES Input/Output AXLAXM Atick xaxis label yaxis label AXQ BARAXL, AXQ AXL, AXM, GAUSS, QXA Access …µBAR Input/Output None BarplotBasis Baud Access …µBESTFIT Input/Output None Access … Ã BINBeep Bestfit Access !L Pict BOX Is the leftshift of the Nkey BinsBlank BOX Access …µBUFLEN Input/Output BuflenBytes #n1 #m1 #n2 #m2 X1, y1 X2, y2 C2P Access … Ã B → RCascfg Case CascmdHelp Ceil CentrXunit Nunit Symb CEILsymb FLOOR, IP, RND, Trnc Chinrem Cholesky Choose Command ResultCHR Circ CksmNUM, POS REPL, SIZE, SUB Clear ClkadjCllcd Closeio CLΣ ClusrClvar Cmplx COL→ →COLCOL COL+ ColctCollect Symb1 Symb2 Colσ CombCON Symb COMBsymb ,m COMBn, symb COMBsymb ,symb Cond Rarray constantCarray constant Name IDN Conic Access …µCONIC Input/Output NoneConj Conlib ConstConstants Rarray Carray Symb CONJsymb Cont ConvertCorr X1unitssource X2unitstarget X3unitstarget Access Flags COSCosh COV Crdir CrossCswp …µCR Curl CyclotomicCylin COL+, COL-, Rswp →PX DarcyDate #n, #m →DATE DATE+Dbug →date Ddays DECDecr « program » or program name Dedicace DEFDefine Result See also Delalarm DEGDegree Name=exp Namename Name =expname Delay RCLALARM, StoalarmDelkeys CR, OLDPRT, PRLCD, PRST, PRSTC, PRVAR, PR1 Access …µDEPND Input/Output DepndDepth Xkey1, ... ,xkey n Dervx DerivDesolve Access …µDETACH Input/Output DETDetach Attach →DIAG DIAG→Diagmap Diff Diffeq DIR Access …µDIFFEQ Input/OutputDisp Dispxy DistribObj List FREEZE, HALT, INPUT, Prompt DIV DIV2DIV2MOD CURL, Hess Divis DivmodDivpc DIV2 TAYLOR0, TAYLR, Series DERIV, DERVX, DESOLVE, ∂Until testclause END END Doerr ErrorDolist List List n « program » Results Command Name List n+1 DomainDosubs SIGNTAB, Tabvar List « program » Command Name DOTDOLIST, ENDSUB, NSUB, Stream CNRM, CROSS, DET, Rnrm Access …µDRAW Access …µDRAX Input/Output NoneDraw DRAW3DMATRIX Droite DropDROP2 Lagrange Dropn DtagDUP DUP2 Dupdup Dupn Editb EditEgcd EGV EgvlElse END Endsub ENGEPSX0 Sign mantissa E sign exponent Eqnlib EQWEQ→ Erase ERR0 ErrmErrn Euler Eval ExlrObj See above →NUM EXP EXP&LNEx,y = excosy + iexsiny EXP2POW EXP2HYPExpan Expand ExpandmodCOLCT, EXPAND, ISOL, QUAD, Show Result X2+X Expfit ExplnExpm Eyept F0λ FactFactor …µF0λ Factors FactormodModsto Fanning Access …µFANNINGFAST3D Access …µFAST3D Input/Output None Access ! Test LL FC ? CFcoef FC? Fdistrib FFTCF, FC?, FS? FS?C, SF Distrib Findalarm Access …µFINISHFiler Finish Flasheval FloorFONT6 Xunit Nunit Symb FLOORsymb FONT7 FONT8FONT→ →FONT For Fourier FreeFreeze Xunit Yunit Symb FPsymb Froots FS?Display Area Value Code CLLCD, DISP, Halt Function FS?CCF, FC?, FC?C, FS?C, SF Fxnd Access …µFUNCTIONExlr Gamma GaussGbasis AXQ, QXA GCD GcdmodGET GCDMOD, EGCD, IEGCD, LCM Objget GetiGETI, PUT, Puti GOR GradGET, PUT, Puti #n #m Grob1 Gramschmidt GraphGreduce DEG, RAD Access …µGRIDMAP Input/Output None Access …µ→GROBGridmap →GROB Grob GrobaddGxor →LCD, LCD→ Hadamard HalftanHalt GOR, REPL, SUB Head HEADER→→HEADER Help Hermite HessHEX CURL, DIV Hilbert Histogram Access …µHISTPLOT Input/Output None HistplotHMS HMS+ HMS→ →HMS… & 9L HMS + … &9L HMS → Horner HomeIabcuv Ibasis IbernoulliIBP ABCUV, Iegcd Ichinrem IDNResults See also Chinrem IDIV2 IegcdDIV2, Iquot Ax+by=c Case IferrELSE, END, IFERR, then ∑ Y k e Ifft IFT IfteIlap Obj It depends Image LAP, Lapl…ßIM Rarray Carray Symb IMsymb Incr IndepInform Global Global xstart xend Resets Title Format Resets Init → valsInput Init INT Stack prompt Commandline prompt ResultPROMPT, STR→ Integer IntvxINV INTVX, Risch Invmod Command INVMOD2 ResultIquot Iremainder IsolIsom Symb1 Global Symb2 ISPRIME? JordanMkisom NEXTPRIME, Prevprime KER KerrmKEY BASIS, Image Keyeval Access …µKEYEVAL Input/Output→KEYTIME KEYTIME→ KgetKill Label Access …µ→LANGUAGE Input/Output LagrangeLANGUAGE→ →LANGUAGE LAP LaplLast Objn Obj1 Lastarg LCD→→LCD LCM Lcxm Ldec Lgcd LibevalLibs HERMITE, Tchebycheff Lim LimitLIN Title, nlib, nport, ...,title, nlib, nport Line ΣlineLinfit Model Form of Expression Linin LinsolveLIST→ →LIST Πlist ListΣlist Access …¹ ¹is the rightshift of the Qkey Lncollect LnameLNP1 Local LOGLn x + Symb LNP1symb Access !Ø Input/Output Logfit Access …µLR Input/Output Full Command and Function Reference 3139LSQ Intercept x Slope x Lvar MADDET, INV Lname Access …µMAP Input/Output MainMant MAP Access …µ↓MATCH Input/Output Access …µ↑MATCH↑MATCH Symb Symb symb Maths MatrMAX Symb Symb , symb Maxr MaxσMcalc Input/Output See also Mean MEMMenu BINS, MAXΣ, MINΣ, SDEV, TOT, VAR Menuxy RCLMENU, Tmenu Merge MINMinehunt MENU, Tmenu MINIFONT→ →MINIFONTMinit Minr Minσ MitmMkisom 00000000000E-499 MOD ModstoModular Mod y Molwt MrootMsgbox Name Or xunit String Mslv Msolvr Multmod Muser→NDISP EQNLIB, MCALC, MINIT, MITM, MROOT, MSLV, Muser Access …ß NEG ßis the rightshift of the 1key NdistNdupn NEG Next NewobNextprime Access ! Test L not Is the leftshift of the Nkey NIPNot Noval Nsub →NUMNUM …µNΣ Numy NumxOBJ→ OCT OFFOldprt … &NL OBJ → Access …µOPENIO Access …µOLDPRTOpenio Order OverMemory Directory Lorder is the leftshift of the Nkey Global1 ... globaln P2C PA2B2Parametric Xmin, ymin, xmax, ymax, indep, res, axes, ptype, depend Access …µPARITY Input/Output Parity Parsurface Partfrac Path PcarPcoef Home directoryname 1 ... directoryname n Pcontour Access …µPCONTOUR Input/Output NonePcov Pdim PerinfoPerm Xmax, ymax Pertbl PevalPgdir Pick Pict Command Puts the name Pict on the stack PictPicture Pinit Access …µPKT PIX?Pixoff Pixon Plot PlotaddPmax Pmin Pmini PolarFinds the minimal polynomial of a matrix An nxn matrix a Access …µPOLAR PolynomialPOP Form of Current Plotting Action Equation Input An expression raised to a power POSPotential Powexpand Powmod PR1 Predv Predx…µPR1 Object Predy Preval Prevprime PrlcdPrompt Promptsto Proot PropfracGlobal→ Prompt STO Prst PrstcPrvar Name Name1 name2 Nport global Psdev PSIPsi MEAN, PCOV, PVAR, SDEV, TOT, VAR Ptayl PtpropPurge Symb String or x or xunit or name Push PUTGlobal Global1 ... globaln CLEAR, CLVAR, NEWOB, Pgdir This command sequence PutiObj put List Obj put List Name Pvars PvarMEAN, PCOV, PSDEV, SDEV, VAR Access …µPVARS Input/Output Nport namebackup MemoryPview Pwrfit →Qπ PX→C+ c/d*i Quad ̟ + c/ d* ̟+ c/ d LQ, LSQ Quot QuoteArithmetic, !ÞPOLYNOMIAL !« Quotient of the Euclidean division QXA RADRand Rank Access …µRATIO RanmRatio LQ, LSQ, QR Rceq RCIRcij Steq Rclalarm RCL FINDALARM, Stoalarm RclfRclkeys Rclmenu Rclvx RclσRcws RDM COMB, PERM, Rand RDZ…ßL RE Recn RectRecv REsymb Remainder RenameQuot New name Old name Reorder RepeatRepl END, While Plot Type Default Interval RESString target String String result Restore Backup To restore aResultant Slopefield Rewrite RevlistRisch RKF Rkferr Rkfstep Problem for a differential equationIs the rightshift 3key RLB RNDRLB, RR, RRB RNDsymb Rnrm RollRolld Romupload Root ROTROW 3207 ROW→ ROW+→ROW Access … ÃL Byte RRB Is the rightshift of the 3key RPLRRB RL, RLB, RRB Rref Rref Rrefmod RRK − 2 t + t 2 Rrkstep RSD RsberrRKF, RKFERR, RKFSTEP, RRK, Rsberr Access … Ã R → B RswpRules DET, IDN Same →R, IM, RE180/̟x →Dsymb Access …µSCALEH Input/Output SbrkScale Scaleh Scatter ScatrplotAUTO, SCALEH, Xrng Access …µSCATTER Input/Output None SchurSCI Sclσ Sconj ScrollSdev Send Series SEQDOSUBS, Stream Server Seval Show SidensSigma X1/cm3 Access !ÖDERIV L Access !ÖDERIV LLSigmavx Sign Signtab SIMP2SIGNsymb ABS, MANT, Xpon Simplify SINSincos Sin z Sinh SinvSize Sinh z SLB SlopefieldString Integer List Vector Symb Grob Snrm SnegNEG, SCONJ, Sinv Solve Solveqn Solvevx SolverSort Sphere SradSquare Analytic Function Returns the square of the argument SQsymb SRB SrecvCOND, SNRM, Trace ASR, SL, SLB, SR Access …µSRECV SreplSST SST↓ STD StartStep Access …µSTIME StepSteq Stime Stoalarm Access Input/OutputSTO Buflen Access …µSTOF StofStokeys Óis the rightshift of the 9 key Stovx StoreSTO+ STO/, + Stoσ STR→→STR DTAG, EQ→, LIST→, OBJ→, →STR Stream StrmSturm List Obj Result Sturmab StwsSUB Sturmab Subst SubtmodX1, y1 X2, y2 CHR, GOR, GXOR, NUM, POS, REPL, Size SVD SVLSwap DIAG→, MIN, SVL Sylvester SysevalSYST2MAT Tabval 100 yX, symb Symb 1, symb Tabvar →TAGTail →ARRY TAN TAN2CS2TAN2SC Tan z TAN2SC2 TanhTanh z TANHsymb TAYLOR0 TaylrTchebycheff HERMITE, Legendre Tcollect TdeltaTests TDELTAsymb1, symb2 Teval TexpandText Then Ticks Time→TIME Tinc Tlin TlineTINCsymb1, symb2 SIMPLIFY, TCOLLECT, Texpand Tmenu TOTTrace Tran Transio TrigEffect BAUD, CKSM, Parity Trigcos TrigoTrigsin Trigtan Trnc TRNCONJ, Tran Trunc TruthTRNCz TRNCsymb Tsimp Access …µTRUTH Input/Output NoneTstr Tvars TVMTvmbeg Tvmend Builtin Commands TypeUbase Object Type Number User objects Ufact UFL1→MINIFUnassign Unassume →UNIT UnbindUnpick Unrot UntilUpdir Utpc Utpf UtpnUTPF, UTPN, Utpt UTPC, UTPN, Utpt Uval UtptUVALsymb Flag -16 clear Rectangular mode Flag -16 set Polar mode € y Coordinate System -16, Complex ModeX1, x2 X1, x2, ..., xn Xn-2 Vandermonde VAR Access …µVERSION Input/Output VarsVER Version Variable name Contents opened in the command line Editor Variable name Contents opened in the most suitable EditorVisit Visitb Vtype Access ! L in Wait Is the leftshift of the NkeyWait Wireframe WhileWhile testclause Repeat loopclause END While Repeat Wslog Access …µWSLOG Access …µΣX Input/OutputΣX2 Log4 ... log1 ΣX2 XcolXget Xmit Xnum Access …µXMITXOR Xpon XputXPONsymb MANT, Sign Command XQ.3658 Results 1829/5000 Command XQ.3658 Results √19/142Xrecv Xrng Access …µXSEND XsendXserv Input/Output RPN Xvol XxrngΣXY ΣX*Y ΣY2 ΣY2Ycol …µΣY Yslice YrngAUTO, PDIM, PMAX, PMIN, Xrng Yvol YyrngZeros EYEPT, XVOL, XXRNG, YYRNG, Zvol Power Access QZfactor Zvol Where √ Square RootZsymb Symbz SQ, , Isol Access …Á Áis the rightshift of the Ukey Integrate? Undefined Lower limit, upper limit, integrand, name ∞ Infinity SummationSigma Plus Results -π/2 Access …µΣ+ Input/Output Access …µΣ Input/OutputSigma Minus X 2, …, x m 1, …, x 1 m x n 1, … , x n m ∂ Derivative Factorial14159265359… Symb Name Xunit Percent Unit attachmentXy/100 Symb,x Less than « » Program delimitersType Object Description ≤ Less than or Equal #n1 #n2 Greater than ≥ Greater than or Equal ≠ Not equal Multiply ≠ symb + Add Subtract Divide = Equal Y1/unit == Logical Equality Store → Create LocalDEFINE, RCL, →, STO … É Semicolon CLEAR, DROP, DROPN, DROP2 CAS Settings Selecting CAS SettingsPoints to note when choosing settings CAS directory, Casdir Computer Algebra System Using the CAS Examples and HelpCompatibility with Other Calculators Extending the CAS Computer algebra command categories listed by menu Arithmetic commandsAlgebra commands, …× Arithmetic Integer commands, !ÞINTEGER Arithmetic Permutation commands, !Þ Permutation Arithmetic Modulo commands, !Þ ModuloOther Arithmetic commands, !Þ Calculus commands Exp and Lin commands, !Ð Matrixrelated commandsCreate, !Ø Create Operations, !Ø Operations Quadratic form, !Ø Quadratic Form Linear Systems, !Ø Linear SystemsLinear Applications, !Ø Linear Appl Eigenvectors, !Ø Eigenvectors Symbolic solve commands, !Î Trigonometry commandsOther Trigonometry commands, …Ñ Hyperbolic, …Ñ Hyperbolic Convert commands, !Ú Unit conversion tools, !Ú Units ToolsBase conversion tools, !Ú Base Trigonometric conversions, !Ú Trig Conv Other CAS operations, …µ Matrix convert, !Ú Matrix Convert These commands display menus or lists of CAS operations CAS menu commands, …µCAS utility operations Equation Reference Equation Reference FLUIDS, 24 *********************3 Columns and Beams Variable DescriptionΣcr Critical stress Σmax Maximum stress Internal bending moment at Elastic Buckling 1 Eccentric Columns 1Equations Example Simple Slope 1 Simple Deflection 1Equation Simple Moment 1 Solution V=624.387lbfSimple Shear 1 Cantilever Slope 1 Cantilever Deflection 1Cantilever Moment 1 Solution V=200lbf Equation Reference Cantilever Shear 1 Relative permittivity ElectricityRelative permeability Ohm’s Law and Power 2 Coulomb’s Law 2 Wire Resistance 2 Solution V1=80VSolution I1=5.6250A Voltage Divider 2 Series and Parallel R 2 Solution R=0.175Series and Parallel C 2 Solution V=50V Series and Parallel L 2Capacitive Energy 2 Inductive Energy 2 RLC Current Delay 2 Solution q=0.0020C Equation ReferenceDC Capacitor Current 2 Capacitor Charge 2 Solution V=3.2968V DC Inductor Voltage 2RC Transient 2 RL Transient 2 Solution I=0.0072A Resonant Frequency 2Plate Capacitor 2 Cylindrical Capacitor 2,19 Solenoid Inductance 2 Toroid Inductance 2 Sinusoidal Voltage 2 FluidsSinusoidal Current 2 Pressure at Depth 3 Bernoulli Equation 3Reynolds number Initial and final velocities Flow with Losses 3 Forces and Energy Flow in Full Pipes 3 Linear Mechanics 4 Centripetal Force 4 Angular Mechanics 4Hooke’s Law 4 1D Elastic Collisions 4 Drag Force 4Law of Gravitation 4 MassEnergy Relation 4 Gases Ideal Gas Law 5 Solution Vf=21 Ideal Gas State Change 5Isothermal Expansion 5 Polytropic Processes 5 Real Gas Law 5 Real Gas State Change 5 Heat Transfer Kinetic Theory 5 Thermal Expansion 6 Heat Capacity 6Conduction 6 Convection 6 Conduction + Convection 6 Magnetism Black Body Radiation 6Fba Ia, Ib Straight Wire 7 Force between Wires 7 Magnetic B Field in Solenoid 7 Solution B=0.0785TMagnetic B Field in Toroid 7 Motion Object in Free Fall 8 Linear Motion 8Projectile Motion 8 Angular Motion 8 Circular Motion 8Terminal Velocity 8 Escape Velocity 8 Optics Law of Refraction 9 Critical Angle 9 Brewster’s Law 9 Solution n2=1.5000 Spherical Reflection 9Spherical Refraction 9 Thin Lens 9 Oscillations Simple Pendulum 10 MassSpring System 10Example Given L=15cm Torsional Pendulum 10 Conical Pendulum 10Simple Harmonic 10 Plane Geometry Ellipse 11 Circle 11Equations Example Rectangle 11 Regular Polygon 11 Circular Ring 11 Triangle 11 Solid Geometry Cone 12 Cylinder 12 Parallelepiped 12 Sphere 12 Solid State Devices Saturation current density Drawn mask length PN Step Junctions, orDrawn gate length Nmos Transistors, or Channel length JFETs PN Step Junctions 13 Nmos Transistors 13 VDS Bipolar Transistors 13 JFETs 13 Xdmax = ⋅ Vbi VGS + VDS Maximum principal normal stress Stress AnalysisMinimum principal normal stress Shear Stress 14 Normal Stress 14Stress on an Element 14 Mohr’s Circle 14 Example Transverse Waves 15,1 WavesLongitudinal Waves 15 Sound Waves 15 References Page Development Library Development Library Command Reference Obj StringObj1 … objn Symb Obj1, ...,objn Development Library BetaTesting String Obj Debug string Error listString Obj Code String Library Object String String Error list Edited stringLibrary n LC~C Ey,z.Et →LST Obj … obj Obj 1, ...,obj n Pokearm Obj 1 … obj n Obj 1, ...,obj n →S2 String1 String2Returns String Global Crlib Create Library Command Xlib Extension program Masd The Machine Language and System RPL Compiler IntroductionStarting Masd Modes Format of the error list ErrorsError messages Message Description Links Labels Extable Constants Expressions Operator Priority Macros and includes Compilation directive Filename conventionsDirective Description !DBGINF directive Docstr CPU architecture Saturn ASM modeBit registers New instructions Other notesSkips Skips instructions Equivalents These instructions Are equivalent to Tests Saturn instructions syntax Syntax Example Syntax Example DReg=hh See above. This is only valid in emulated Saturn Places the value of Exp in the code, on x nibbles CARRY0 003AA Autousertest ARM mode ARM architecture Instruction set Description Form Operation Assembler Action Flags Armsat instruction Offset ElementREG a REG B REG C REG D REG R0 REG R1 REG R2 REG R3 REG R4 System RPL mode InstructionsReals and system binary Unnamed local variables Tokens DefinesToken Description Code LC 001 Gosbvl Outcinrtn ?CBIT=1.6 Turnmenuoff LC 80100 Armsat Disassemblers Level Entry Point Library Extable LibraryNop String String 1, ...,string n Error and Status Messages A1 Messages Listed AlphabeticallyMessage Meaning # hex C0C A2 Error and Status Messages Error and Status Messages A3 A4 Error and Status Messages Σdat Error and Status Messages A5 A6 Error and Status Messages Error and Status Messages A7 C0EC0B C0D A8 Error and Status Messages Error and Status Messages A9 # hex Message General Messages A10 Error and Status Messages # hex Message Error and Status Messages A11 OutofMemory Prompts Stack Errors and Messages A12 Error and Status MessagesObject Editing Messages Equation Writer Application Messages # hex Message FloatingPoint Errors Error and Status Messages A13Array Messages Statistics Messages Mode and Plot Input Form Prompts A14 Error and Status Messages Error and Status Messages A15 # hex Message 70F A16 Error and Status Messages 73F Error and Status Messages A17 75F A18 Error and Status Messages 78F Error and Status Messages A19 A20 Error and Status Messages Advanced Statistics Messages Error and Status Messages A21 80F A22 Error and Status Messages 82F Error and Status Messages A23 85F A24 Error and Status Messages 87F Statistics Help Messages Error and Status Messages A25HP Solve Application Messages # hex Message Unit Management PrintingTime Messages Programmer’s Doerr Error and Status Messages A27 A28 Error and Status Messages System Flags Choose Box Prompts Error and Status Messages A29 A30 Error and Status Messages Error and Status Messages A31 A32 Error and Status Messages Prompts Error and Status Messages A33 A34 Error and Status Messages Error and Status Messages A35 Statistics Prompts Time and Alarm Prompts A36 Error and Status Messages Error and Status Messages A37 Symbolic Application Prompts A38 Error and Status Messages Error and Status Messages A39 Plot Application Prompts A40 Error and Status Messages Error and Status Messages A41 A42 Error and Status Messages Solve Application Prompts Error and Status Messages A43 A44 Error and Status Messages Error and Status Messages A45 CAS Messages A46 Error and Status Messages Error and Status Messages A47 A48 Error and Status Messages Filer Application MessagesDF0A DF0B DF0C DF0D DF0E DF0F DF1A DF1B DF1C DF1D DF1E DF1F Error and Status Messages A49 Constants Library Messages A50 Error and Status Messages Equation Library MessagesMinehunt Game Prompts MultipleEquation Solver Messages Error and Status Messages A51 Periodic Table MessagesFinancial Solver Messages Development Library and Miscellaneous Messages A52 Error and Status Messages Units Tables of Units and Constants B1 B2 Tables of Units and Constants Tables of Units and Constants B3 B4 Tables of Units and Constants Tables of Units and Constants B5 Constant Full Name Value in SI Units Properties of Elements B6 Tables of Units and Constants System Flags Flag DescriptionNot used System Flags C1 C2 System Flags System Flags C3 C4 System Flags System Flags C5 C6 System Flags System Flags C7 Internal use only /0 occurred C8 System Flags User Flags System Flags C9Page Reserved Variables D1 Contents of the System Reserved Variables ΒENTER Reserved Variables D3 Exited D4 Reserved Variables Reserved Variables D5 MHpar MparN1, n2 Nmines BAR, etc Reserved Variables D7 Prtpar D8 Reserved Variables S1, s2 Reserved Variables D9 Parameter Description Default Value Command To use for input into the tableNUMX, Numy D10 Reserved Variables Statistical Matrix for Variables 1 to m Var1 var2 … varmReserved Variables D11 EXPFIT, PWRFIT, or Logfit D12 Reserved Variables Casdir Reserved Variables Modulo D14 Reserved Variables Object Type Size bytes Object SizeTechnical Reference E1 Pattern Antiderivative Symbolic IntegrationE2 Technical Reference Technical Reference E3 →DEF Expansions E4 Technical Reference Order Operation Technical Reference E5 International Standard publication No. ISO 31/l197 8 E E6 Technical Reference Group 1 Commands that cannot parallel process Group 2 Commands that must use Dolist to parallel processGeneral rules for parallel processing Parallel Processing with Lists F1 Group 5 Commands that set modes / states Group 6 Oneargument, oneresult commandsGroup 4 ADD and + F2 Parallel Processing with Lists Group 7 Two argument, one result commands Group 8 Multipleargument, oneresult commandsGroup 9 Multipleresult commands Group 10 Quirky commands Using Dolist for Parallel Processing F4 Parallel Processing with Lists $ & C $ & D$ & F $ & + Keycode Keystroke Definition ¥ ! &I@ & ³ @ & O ~@ & O @%VARNAME% = varname ~@ & Í @ &†Keyboard Shortcuts G3 G4 Keyboard Shortcuts Syntax Example Menu NumbersMenuNumber Table H1 Menus 0 through H2 The MenuNumber Table MenuNumber Table H3 Menus 118 through H4 The MenuNumber Table BuiltIn Library Menus Menus 178 throughMenuNumber Table H5 Page Key ALPHARS2 MTH NXT Prob Command MenuPath Table+ key Command Type Library Size Keys Menu First I2 The Command MenuPath Table MTH List Arith Modul«MODULAR» Addtoreal CAT Algb I4 The Command MenuPath Table LS&MODE Flag PRG Test NXT NXT PRG NXT Modes Flag ChinremPRG NXT CHR I6 The Command MenuPath Table CAT Delalarm PRG NXT NXT Time Alrm DelayRS&TIME NXT PRG NXT NXT Time NXT I8 The Command MenuPath Table PRG NXT NXT Error Iferr «POLYNOMIAL» EGVMTH Matrx NXT Else I10 The Command MenuPath Table I11 I12 The Command MenuPath Table Calc Deriv NXT «INTEGER»PRG Brch NXT «DIFF» NXT NXT I14 The Command MenuPath Table I15 I16 The Command MenuPath Table I17 I18 The Command MenuPath Table I19 I20 The Command MenuPath Table I21 I22 The Command MenuPath Table I23 I24 The Command MenuPath Table I25 I26 The Command MenuPath Table I27 I28 The Command MenuPath Table Matrices Creat NXT NXT MTH Matrx Make NXT NXT DUP Menuxy VersionCAT Vtype XLIB~ I30 The Command MenuPath Table SLV NXTAlphalse MTH NXT Const «CONSTANTS» Σline ΣlistPRG Test «TESTS» NXT →ALG I32 The Command MenuPath Table Character Codes Code DescriptionAscii Character Codes and Translations J1 Code Trans. Description J2 Ascii Character Codes and Translations Index Alpha keyboard Calculator 59, 531 375 Preserving calculator status Flags 132 Last argument Memory Nested structures 545 Programs Range 3115 Serial communications 237, D3 Tagged objects UPs