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IEVref:103-02-02ID:
Language:enStatus: Standard
Term: root-mean-square value
Synonym1: RMS value
[Preferred]
Synonym2: quadratic mean
[Preferred]
Synonym3:
Symbol:
Definition: quantity representing the quantities in a finite set or in an interval,

  1. for n quantities x 1 , x 2 , x n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaadIhadaWgaaWcba GaaGymaaqabaGccaGGSaGaaGjbVlaadIhadaWgaaWcbaGaaGOmaaqa baGccaGGSaGaaGjbVlaaykW7cqWIMaYscaaMc8UaaGPaVlaaysW7ca WG4bWaaSbaaSqaaiaad6gaaeqaaaaa@4713@ , by the positive square root of the mean value of their squares:

    X q = ( 1 n ( x 1 2 + x 2 2 ++ x n 2 )) 1/2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaadIfadaWgaaWcba qcLboacaqGXbaaleqaaOGaeyypa0ZaamWaaeaadaWcaaqaaKqzafGa aGymaaGcbaGaamOBaaaacaGGOaGaamiEamaaDaaaleaajug4aiaaig daaSqaaKqzGdGaaGOmaaaakiabgUcaRiaadIhadaqhaaWcbaqcLboa caaIYaaaleaajug4aiaaikdaaaGccqGHRaWkcaaMc8UaaGjbVlaayk W7cqWIMaYscaaMc8UaaGPaVlaaysW7cqGHRaWkcaWG4bWaa0baaSqa aiaad6gaaeaajug4aiaaikdaaaGccaGGPaaacaGLBbGaayzxaaWaaW baaSqabeaajug4aiaaigdacaGGVaGaaGOmaaaaaaa@5F01@

  2. for a quantity x depending on a variable t, by the positive square root of the mean value of the square of the quantity taken over a given interval ( t 0 , t 0 +T) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaacUfacaWG0bWaaS baaSqaaKqzGdGaaGimaaWcbeaakiaacYcacaaMe8UaamiDamaaBaaa leaajug4aiaaicdaaSqabaGccqGHRaWkcaWGubGaaiyxaaaa@418C@ of the variable:

    X q = ( 1 T t 0 t 0 +T ( x(t) ) 2 dt ) 1/2 MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadIfadaWgaaWcbaqcLboacaqGXbaaleqaaOGaeyypa0ZaamWaaeaadaWcaaqaaKqzafGaaGymaaGcbaGaamivaaaadaWdXaqaamaadmaabaGaamiEaiaacIcacaWG0bGaaiykaaGaay5waiaaw2faamaaCaaaleqabaGaaGOmaaaaaeaacaaMi8UaamiDamaaBaaameaacaaIWaaabeaaaSqaaiaayIW7caWG0bWaaSbaaWqaaiaaicdaaeqaaSGaey4kaSIaamivaaqdcqGHRiI8aKqzafGaaiizaOGaamiDaaGaay5waiaaw2faamaaCaaaleqabaqcLboacaaIXaGaai4laiaaikdaaaaaaa@553C@

Note 1 to entry: The root-mean-square value of a periodic quantity is usually taken over an integration interval the range of which is the period multiplied by a natural number.

Note 2 to entry: The root-mean-square value of a quantity is denoted by adding the subscript q to the symbol of the quantity.

Note 3 to entry: The abbreviation RMS was formerly denoted as r.m.s. or rms, but these notations are now deprecated.


Publication date:2017-07
Source:
Replaces:103-02-02:2009-12
Internal notes:
CO remarks: 2017-08-25: Added

tag before list. LMO

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