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Notes for this derivation:
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Index  Inference Rule  Input latex  Feeds latex  Output latex  step validity  dimension check  unit check  notes 

1  declare initial expr 



no validation is available for declarations 
5900595848:

5900595848:


6  substitute RHS of expr 1 into expr 2 



valid 
3131111133:
0404050504: 1293923844: 
3131111133:
0404050504: 1293923844: 

2  declare initial expr 



no validation is available for declarations 
0404050504:

0404050504:


5  substitute RHS of expr 1 into expr 2 



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 



LHS diff is pdg9491*(pdg4201 + pdg6235) RHS diff is (pdg4201 + pdg6235)/pdg4201 
3131111133:
2131616531: 
3131111133:
2131616531: 

3  declare initial expr 



no validation is available for declarations 
3131211131:
dimensions are consistent 
3131211131:
N/A 

11  declare final expr 



no validation is available for declarations 
3121513111:

3121513111:


7  substitute RHS of expr 1 into expr 2 



valid 
1293923844:
0934990943: 3121513111: 
1293923844:
0934990943: 3121513111: 

4  declare initial expr 



no validation is available for declarations 
3131111133:

3131111133:


9  divide both sides by 



valid 
2131616531:
2113211456: dimensions are consistent 
2131616531:
2113211456: N/A 

10  substitute RHS of expr 1 into expr 2 



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 
symbol ID  category  latex  scope  dimension  name  value  Used in derivations  references  

1357  variable 
v
\(v\) 
['real'] 

velocity 

80  
3141  constant 
\pi
\(\pi\) 
['real']  dimensionless  pi 
3.1415 dimensionless 
55  
9491  variable 
T
\(T\) 
['real'] 

period  8  
6235  variable 
f
\(f\) 
real  dimensionless  proportionality constant 

5  
4201  variable 
f
\(f\) 
['real'] 

frequency  8  
5321  variable 
k
\(k\) 
['real'] 

angular wavenumber  13  
1115  variable 
\lambda
\(\lambda\) 
['real'] 

wavelength  5  
2321  variable 
\omega
\(\omega\) 
['real'] 

angular frequency  21 