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review derivation: frequency relations

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Index Inference Rule Input latex Feeds latex Output latex step validity dimension check unit check notes
1 declare initial expr
  1. 5900595848; locally 3293094:
    \(k = \frac{\omega}{v}\)
    \(pdg_{5321} = \frac{pdg_{2321}}{pdg_{1357}}\)
no validation is available for declarations 5900595848:
5900595848:
6 substitute RHS of expr 1 into expr 2
  1. 3131111133; locally 8482459:
    \(T = 1 / f\)
    \(pdg_{9491} = \frac{1}{pdg_{4201}}\)
  2. 0404050504; locally 3294004:
    \(\lambda = \frac{v}{f}\)
    \(pdg_{1115} = \frac{pdg_{1357}}{pdg_{4201}}\)
  1. 1293923844; locally 3993940:
    \(\lambda = v T\)
    \(pdg_{1115} = pdg_{1357} pdg_{9491}\)
valid 3131111133:
0404050504:
1293923844:
3131111133:
0404050504:
1293923844:
2 declare initial expr
  1. 0404050504; locally 3294004:
    \(\lambda = \frac{v}{f}\)
    \(pdg_{1115} = \frac{pdg_{1357}}{pdg_{4201}}\)
no validation is available for declarations 0404050504:
0404050504:
5 substitute RHS of expr 1 into expr 2
  1. 3132131132; locally 8374556:
    \(\omega = \frac{2\pi}{T}\)
    \(pdg_{2321} = \frac{2 pdg_{3141}}{pdg_{9491}}\)
  2. 5900595848; locally 3293094:
    \(k = \frac{\omega}{v}\)
    \(pdg_{5321} = \frac{pdg_{2321}}{pdg_{1357}}\)
  1. 0934990943; locally 8394853:
    \(k = \frac{2 \pi}{v T}\)
    \(pdg_{5321} = \frac{2 pdg_{3141}}{pdg_{1357} pdg_{9491}}\)
LHS diff is 0 RHS diff is (pdg2321*pdg9491 - 2*pdg3141)/(pdg1357*pdg9491) 3132131132: dimensions are consistent
5900595848:
0934990943:
3132131132: N/A
5900595848:
0934990943:
8 multiply both sides by
  1. 3131111133; locally 8482459:
    \(T = 1 / f\)
    \(pdg_{9491} = \frac{1}{pdg_{4201}}\)
  1. 0005749291:
    \(f\)
    \(pdg_{6235}\)
  1. 2131616531; locally 8341200:
    \(T f = 1\)
    \(pdg_{4201} pdg_{9491} = 1\)
LHS diff is pdg9491*(-pdg4201 + pdg6235) RHS diff is (-pdg4201 + pdg6235)/pdg4201 3131111133:
2131616531:
3131111133:
2131616531:
3 declare initial expr
  1. 3131211131; locally 9214650:
    \(\omega = 2 \pi f\)
    \(pdg_{2321} = 2 pdg_{3141} pdg_{4201}\)
no validation is available for declarations 3131211131: dimensions are consistent
 3131211131: N/A
11 declare final expr
  1. 3121513111; locally 2934848:
    \(k = \frac{2 \pi}{\lambda}\)
    \(pdg_{5321} = \frac{2 pdg_{3141}}{pdg_{1115}}\)
no validation is available for declarations 3121513111:
3121513111:
7 substitute RHS of expr 1 into expr 2
  1. 1293923844; locally 3993940:
    \(\lambda = v T\)
    \(pdg_{1115} = pdg_{1357} pdg_{9491}\)
  2. 0934990943; locally 8394853:
    \(k = \frac{2 \pi}{v T}\)
    \(pdg_{5321} = \frac{2 pdg_{3141}}{pdg_{1357} pdg_{9491}}\)
  1. 3121513111; locally 2934848:
    \(k = \frac{2 \pi}{\lambda}\)
    \(pdg_{5321} = \frac{2 pdg_{3141}}{pdg_{1115}}\)
valid 1293923844:
0934990943:
3121513111:
1293923844:
0934990943:
3121513111:
4 declare initial expr
  1. 3131111133; locally 8482459:
    \(T = 1 / f\)
    \(pdg_{9491} = \frac{1}{pdg_{4201}}\)
no validation is available for declarations 3131111133:
3131111133:
9 divide both sides by
  1. 2131616531; locally 8341200:
    \(T f = 1\)
    \(pdg_{4201} pdg_{9491} = 1\)
  1. 0008837284:
    \(T\)
    \(pdg_{9491}\)
  1. 2113211456; locally 9380032:
    \(f = 1/T\)
    \(pdg_{4201} = \frac{1}{pdg_{9491}}\)
valid 2131616531:
2113211456: dimensions are consistent
 2131616531:
2113211456: N/A
10 substitute RHS of expr 1 into expr 2
  1. 2113211456; locally 9380032:
    \(f = 1/T\)
    \(pdg_{4201} = \frac{1}{pdg_{9491}}\)
  2. 3131211131; locally 9214650:
    \(\omega = 2 \pi f\)
    \(pdg_{2321} = 2 pdg_{3141} pdg_{4201}\)
  1. 3132131132; locally 8374556:
    \(\omega = \frac{2\pi}{T}\)
    \(pdg_{2321} = \frac{2 pdg_{3141}}{pdg_{9491}}\)
LHS diff is 0 RHS diff is 2*pdg3141*(pdg4201*pdg9491 - 1)/pdg9491 2113211456: dimensions are consistent
3131211131: dimensions are consistent
3132131132: dimensions are consistent
 2113211456: N/A
3131211131: N/A
3132131132: N/A
Physics Derivation Graph: Steps for frequency relations

Symbols for this derivation

See also all 227 symbols
symbol ID category latex scope dimension name value Used in derivations references
1357 variable v
\(v\)		 ['real']
  • length: 1
  • time: -1
 velocity 83
6235 variable f
\(f\)		 real dimensionless proportionality constant
  • str_note
5
3141 constant \pi
\(\pi\)		 ['real'] dimensionless pi 3.1415   dimensionless
 72
1115 variable \lambda
\(\lambda\)		 ['real']
  • length: 1
 wavelength 5
2321 variable \omega
\(\omega\)		 ['real']
  • time: -1
 angular frequency 26
9491 variable T
\(T\)		 ['real']
  • time: 1
 period 20
5321 variable k
\(k\)		 ['real']
  • length: -1
 angular wavenumber 13
4201 variable f
\(f\)		 ['real']
  • time: -1
 frequency 8
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