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Diffstat (limited to 'doc/misc/calc.texi')
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diff --git a/doc/misc/calc.texi b/doc/misc/calc.texi index 88103fc0034..f732eff5690 100644 --- a/doc/misc/calc.texi +++ b/doc/misc/calc.texi @@ -28126,47 +28126,15 @@ tell Calc to use a different file for the Calc init file.) @section Logarithmic Units The units @code{dB} (decibels) and @code{Np} (nepers) are logarithmic -units which are typically manipulated differently than standard units. -Calc provides commands to work with these logarithmic units. +units which are manipulated differently than standard units. Calc +provides commands to work with these logarithmic units. Decibels and nepers are used to measure power quantities as well as -field quantities (quantities whose squares are proportional to power). -The decibel and neper values of a quantity are relative to -a reference quantity; for example, the decibel value of a sound -pressure level of -@infoline @math{60 uPa} -@texline @math{60 \mu{\rm Pa}} -relative to -@infoline @math{20 uPa} -@texline @math{20 \mu{\rm Pa}} -(the threshhold of human hearing) is -@infoline @math{20 log10(60 uPa/ 20 uPa) dB = 20 log10(3) dB}, -@texline @math{20 \log_{10}(60 \mu{\rm Pa}/20 \mu{\rm Pa}) {\rm dB} = 20 \log_{10}(3) {\rm dB}}, -which is about -@infoline @math{9.54 dB}. -@texline @math{9.54 {\rm dB}}. -Note that in taking the ratio, the original units cancel and so these -logarithmic units are dimensionless. - -@vindex calc-logunits-power-reference -@vindex calc-logunits-field-reference -The Calc commands for the logarithmic units assume that power quantities -are being used unless the @kbd{H} prefix is used, in which case they assume that -field quantities are being used. For power quantities, Calc uses -@infoline @math{1 mW} -@texline @math{1 {\rm mW}} -as the default reference quantity; this default can be changed by changing -the value of the customizable variable -@code{calc-logunits-power-reference} (@pxref{Customizing Calc}). -For field quantities, Calc uses -@infoline @math{20 uPa} -@texline @math{20 \mu{\rm Pa}} -as the default reference quantity; this is the value used in acoustics -which is where decibels are commonly encountered. This default can be -changed by changing the value of the customizable variable -@code{calc-logunits-field-reference} (@pxref{Customizing Calc}). A -non-default reference quantity will be read from the stack if the -capital @kbd{O} prefix is used. +field quantities (quantities whose squares are proportional to power); +these two types of quantities are handled slightly different from each +other. By default the Calc commands work as if power quantities are +being used; with the @kbd{H} prefix the Calc commands work as if field +quantities are being used. The decibel level of a power @infoline @math{P1}, @@ -28214,6 +28182,20 @@ relative to a reference is defined as @infoline @math{20 log10(F1/F0) dB}. @texline @math{20 \log_{10}(F_{1}/F_{0}) {\rm dB}}. +For example, the decibel value of a sound pressure level of +@infoline @math{60 uPa} +@texline @math{60 \mu{\rm Pa}} +relative to +@infoline @math{20 uPa} +@texline @math{20 \mu{\rm Pa}} +(the threshhold of human hearing) is +@infoline @math{20 log10(60 uPa/ 20 uPa) dB = 20 log10(3) dB}, +@texline @math{20 \log_{10}(60 \mu{\rm Pa}/20 \mu{\rm Pa}) {\rm dB} = 20 \log_{10}(3) {\rm dB}}, +which is about +@infoline @math{9.54 dB}. +@texline @math{9.54 {\rm dB}}. +Note that in taking the ratio, the original units cancel and so these +logarithmic units are dimensionless. Nepers (named after John Napier, who is credited with inventing the logarithm) are similar to bels except they use natural logarithms instead @@ -28236,55 +28218,72 @@ is @infoline @math{ln(F1/F0) Np}. @texline @math{\ln(F_1/F_0) {\rm Np}}. +@vindex calc-lu-power-reference +@vindex calc-lu-field-reference +For power quantities, Calc uses +@infoline @math{1 mW} +@texline @math{1 {\rm mW}} +as the default reference quantity; this default can be changed by changing +the value of the customizable variable +@code{calc-lu-power-reference} (@pxref{Customizing Calc}). +For field quantities, Calc uses +@infoline @math{20 uPa} +@texline @math{20 \mu{\rm Pa}} +as the default reference quantity; this is the value used in acoustics +which is where decibels are commonly encountered. This default can be +changed by changing the value of the customizable variable +@code{calc-lu-field-reference} (@pxref{Customizing Calc}). A +non-default reference quantity will be read from the stack if the +capital @kbd{O} prefix is used. + @kindex l q -@pindex calc-logunits-quantity -@tindex powerquant -@tindex fieldquant -The @kbd{l q} (@code{calc-logunits-quantity}) [@code{powerquant}] +@pindex calc-lu-quant +@tindex lupquant +@tindex lufquant +The @kbd{l q} (@code{calc-lu-quant}) [@code{lupquant}] command computes the power quantity corresponding to a given number of logarithmic units. With the capital @kbd{O} prefix, @kbd{O l q}, the reference level will be read from the top of the stack. (In an -algebraic formula, @code{powerquant} can be given an optional second +algebraic formula, @code{lupquant} can be given an optional second argument which will be used for the reference level.) For example, @code{20 dB @key{RET} l q} will return @code{100 mW}; @code{20 dB @key{RET} 4 W @key{RET} O l q} will return @code{400 W}. -The @kbd{H l q} [@code{fieldquant}] command behaves like @kbd{l q} but +The @kbd{H l q} [@code{lufquant}] command behaves like @kbd{l q} but computes field quantities instead of power quantities. @kindex l d -@pindex calc-dblevel -@tindex dbpowerlevel -@tindex dbfieldlevel +@pindex calc-db +@tindex dbpower +@tindex dbfield @kindex l n -@pindex calc-nplevel -@tindex nppowerlevel -@tindex npfieldlevel -The @kbd{l d} (@code{calc-dblevel}) [@code{dbpowerlevel}] -command will compute the decibel level of a power quantity using the -default reference level; @kbd{H l d} [@code{dbfieldlevel}] will -compute the decibel level of a field quantity. The commands @kbd{l n} -(@code{calc-nplevel}) [@code{nppowerlevel}] and @kbd{H l n} -[@code{npfieldlevel}] will similarly compute neper levels. With the -capital @kbd{O} prefix these commands will read a reference level -from the stack; in an algebraic formula the reference level can be -given as an optional second argument. +@pindex calc-np +@tindex nppower +@tindex npfield +The @kbd{l d} (@code{calc-db}) [@code{dbpower}] command will compute +the decibel level of a power quantity using the default reference +level; @kbd{H l d} [@code{dbfield}] will compute the decibel level of +a field quantity. The commands @kbd{l n} (@code{calc-np}) +[@code{nppower}] and @kbd{H l n} [@code{npfield}] will similarly +compute neper levels. With the capital @kbd{O} prefix these commands +will read a reference level from the stack; in an algebraic formula +the reference level can be given as an optional second argument. @kindex l + -@pindex calc-logunits-add -@tindex lupoweradd -@tindex lufieldadd +@pindex calc-lu-plus +@tindex lupadd +@tindex lufadd @kindex l - -@pindex calc-logunits-sub -@tindex lupowersub -@tindex lufieldsub +@pindex calc-lu-minus +@tindex lupsub +@tindex lufsub @kindex l * -@pindex calc-logunits-mul -@tindex lupowermul -@tindex lufieldmul +@pindex calc-lu-times +@tindex lupmul +@tindex lufmul @kindex l / -@pindex calc-logunits-div -@tindex lupowerdiv -@tindex lufielddiv +@pindex calc-lu-divide +@tindex lupdiv +@tindex lufdiv The sum of two power or field quantities doesn't correspond to the sum of the corresponding decibel or neper levels. If the powers corresponding to decibel levels @@ -28305,13 +28304,13 @@ $$ 10 \log_{10}(10^{D_1/10} + 10^{D_2/10}) {\rm dB}.$$ @end tex @noindent -When field quantities are combined, it often means the -corresponding powers are added and so the above formula might be used. -In acoustics, for example, the decibel sound pressure level is defined -using the field formula but the sound pressure levels are combined -as the sound power levels, and so the above formula should be used. If -two field quantities themselves are added, the new decibel level will be - +When field quantities are combined, it often means the corresponding +powers are added and so the above formula might be used. In +acoustics, for example, the sound pressure level is a field quantity +and so the decibels are often defined using the field formula, but the +sound pressure levels are combined as the sound power levels, and so +the above formula should be used. If two field quantities themselves +are added, the new decibel level will be @ifnottex @example @@ -28349,20 +28348,18 @@ $$ D + 20 \log_{10}(N) {\rm dB}.$$ @end tex @noindent -There are similar formulas for combining nepers. -The @kbd{l +} (@code{calc-logunits-add}) [@code{lupoweradd}] command -will ``add'' two logarithmic unit power levels this way; with the -@kbd{H} prefix, @kbd{H l +} [@code{lufieldadd}] will add logarithmic -unit field levels. Similarly, logarithmic units can be -``subtracted'' with @kbd{l -} (@code{calc-logunits-sub}) -[@code{lupowersub}] or @kbd{H l -} [@code{lufieldsub}]. -The @kbd{l *} (@code{calc-logunits-mul}) [@code{lupowermul}] -and @kbd{H l *} [@code{lufieldmul}] commands will ``multiply'' -a logarithmic unit by a number; the @kbd{l /} -(@code{calc-logunits-divide}) [@code{lupowerdiv}] and -@kbd{H l /} [@code{lufielddiv}] commands will ``divide'' a -logarithmic unit by a number. Note that the reference quantities don't -play a role in this arithmetic. +There are similar formulas for combining nepers. The @kbd{l +} +(@code{calc-lu-plus}) [@code{lupadd}] command will ``add'' two +logarithmic unit power levels this way; with the @kbd{H} prefix, +@kbd{H l +} [@code{lufadd}] will add logarithmic unit field levels. +Similarly, logarithmic units can be ``subtracted'' with @kbd{l -} +(@code{calc-lu-minus}) [@code{lupsub}] or @kbd{H l -} [@code{lufsub}]. +The @kbd{l *} (@code{calc-lu-times}) [@code{lupmul}] and @kbd{H l *} +[@code{lufmul}] commands will ``multiply'' a logarithmic unit by a +number; the @kbd{l /} (@code{calc-lu-divide}) [@code{lupdiv}] and +@kbd{H l /} [@code{lufdiv}] commands will ``divide'' a logarithmic +unit by a number. Note that the reference quantities don't play a role +in this arithmetic. @node Musical Notes, , Logarithmic Units, Units @section Musical Notes @@ -35539,16 +35536,16 @@ should also be added to @code{calc-embedded-announce-formula-alist} and @code{calc-embedded-open-close-plain-alist}. @end defvar -@defvar calc-logunits-power-reference -@defvarx calc-logunits-field-reference +@defvar calc-lu-power-reference +@defvarx calc-lu-field-reference See @ref{Logarithmic Units}.@* -The variables @code{calc-logunits-power-reference} and -@code{calc-logunits-field-reference} are unit expressions (written as +The variables @code{calc-lu-power-reference} and +@code{calc-lu-field-reference} are unit expressions (written as strings) which Calc will use as reference quantities for logarithmic units. -The default value of @code{calc-logunits-power-reference} is @code{"mW"} -and the default value of @code{calc-logunits-field-reference} is +The default value of @code{calc-lu-power-reference} is @code{"mW"} +and the default value of @code{calc-lu-field-reference} is @code{"20 uPa"}. @end defvar @@ -36209,26 +36206,26 @@ keystrokes are not listed in this summary. @r{ v x@: I k T @: @: @:ltpt@:(x,v)} @c -@r{ a b@: l + @: @: @:lupoweradd@:(a,b)} -@r{ a b@: H l + @: @: @:lufieldadd@:(a,b)} -@r{ a b@: l - @: @: @:lupowersub@:(a,b)} -@r{ a b@: H l - @: @: @:lufieldsub@:(a,b)} -@r{ a b@: l * @: @: @:lupowermul@:(a,b)} -@r{ a b@: H l * @: @: @:lufieldmul@:(a,b)} -@r{ a b@: l / @: @: @:lupowerdiv@:(a,b)} -@r{ a b@: H l / @: @: @:lufielddiv@:(a,b)} -@r{ a@: l d @: @: @:dbpowerlevel@:(a)} -@r{ a b@: O l d @: @: @:dbpowerlevel@:(a,b)} -@r{ a@: H l d @: @: @:dbfieldlevel@:(a)} -@r{ a b@: O H l d @: @: @:dbfieldlevel@:(a,b)} -@r{ a@: l n @: @: @:nppowerlevel@:(a)} -@r{ a b@: O l n @: @: @:nppowerlevel@:(a,b)} -@r{ a@: H l n @: @: @:npfieldlevel@:(a)} -@r{ a b@: O H l n @: @: @:npfieldlevel@:(a,b)} -@r{ a@: l q @: @: @:powerquant@:(a)} -@r{ a b@: O l q @: @: @:powerquant@:(a,b)} -@r{ a@: H l q @: @: @:fieldquant@:(a)} -@r{ a b@: O H l q @: @: @:fieldquant@:(a,b)} +@r{ a b@: l + @: @: @:lupadd@:(a,b)} +@r{ a b@: H l + @: @: @:lufadd@:(a,b)} +@r{ a b@: l - @: @: @:lupsub@:(a,b)} +@r{ a b@: H l - @: @: @:lufsub@:(a,b)} +@r{ a b@: l * @: @: @:lupmul@:(a,b)} +@r{ a b@: H l * @: @: @:lufmul@:(a,b)} +@r{ a b@: l / @: @: @:lupdiv@:(a,b)} +@r{ a b@: H l / @: @: @:lufdiv@:(a,b)} +@r{ a@: l d @: @: @:dbpower@:(a)} +@r{ a b@: O l d @: @: @:dbpower@:(a,b)} +@r{ a@: H l d @: @: @:dbfield@:(a)} +@r{ a b@: O H l d @: @: @:dbfield@:(a,b)} +@r{ a@: l n @: @: @:nppower@:(a)} +@r{ a b@: O l n @: @: @:nppower@:(a,b)} +@r{ a@: H l n @: @: @:npfield@:(a)} +@r{ a b@: O H l n @: @: @:npfield@:(a,b)} +@r{ a@: l q @: @: @:lupquant@:(a)} +@r{ a b@: O l q @: @: @:lupquant@:(a,b)} +@r{ a@: H l q @: @: @:lufquant@:(a)} +@r{ a b@: O H l q @: @: @:lufquant@:(a,b)} @r{ a@: l s @: @: @:spn@:(a)} @r{ a@: l m @: @: @:midi@:(a)} @r{ a@: l f @: @: @:freq@:(a)} |