Physics NYC Equation Sheet

Simple Harmonic Motion xF kx= − ( ) cos( )ω φ= +x t A t

22 fTπ

ω π= =

2 LTg

π=

2 mTk

π=

212 vK m=

gU mgh= 21

2sU kx= 21

2totalE K U kA= + = Quantum Physics

hcE hfλ

= =

0 φ= −eV hf 𝐾!"# = 𝑒𝑉!

hpλ

=

( )1 cose

hm c

λ φΔ = −

Δx Δpx ≥ ( ) 2 2

2128n

n hE n EmL

= =

2( ) sin( )n

n xxL L

πψ =

12 2

13.6eVnEEn n

−= =

Waves and Sound

( , ) A cos( )y x t kx tω= ± 2k πλ

=

v fkω

λ= =

Fvµ

=

2 21av 2 F P Aµ ω=

SW( , ) sin( )sin( )y x t A kx tω=

f beat = Δf = f a − f b

avPIA

=

0

10log II

β⎛ ⎞

= ⎜ ⎟⎝ ⎠

f L =v ±vLv vS

!

"##

$

%&& f S

Relativity

0γΔ = Δt t

0

γ=ll

2 2

11 u c

γ =−

21 /−

=−x

xx

' v uvv u c

21 /ʹ′ +

=ʹ′+x

xx

v uvv u c

VAB =VAD +VDB

1+ VADVDBc 2

p = γm v 2 2E mc K mcγ= = +

( ) ( )2 22 2= +E mc pc

Interference and Diffraction sind mθ λ=

( )12sind mθ λ= + sina mθ λ= 2 sinπ

φ θλ

= d

2 sinπβ θ

λ= a

1.22 λθ =D

2max cos 2

I I φ⎛ ⎞= ⎜ ⎟⎝ ⎠

2

maxsin( / 2)

/ 2I I β

β⎛ ⎞

= ⎜ ⎟⎝ ⎠

Constants Speed of sound in air (20°) = 343 m/s

Threshold of hearing: 12 20 1.0 10 W/mI −= ×

Audible range: 20 Hz to 20000 Hz

Visible spectrum: 400 nm to 700 nm 83.00 10 m/sc = ×

191 eV 1.60 10 J−= × 31

e2

9.11 10 kg

0.511 MeV/

mc

−= ×

= 27

p n

2

1.67 10 kg

938 MeV/

m m

c

−= = ×

=

34

15

6.63 10 J s 4.14 10 eV sh −

−

= × ⋅

= × ⋅ 29.81 m/sg =

1 13.6 eVE = − for hydrogen atom

e = 1.6 x 10-19 C