## 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

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