Physics 122 Equations
n1 sinθ 1 = n2 sinθ 2
θr = θi
#n &
θ c = sin −1 % 2 (
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2
d x
= −kx
dt 2
x(t) = A cos(ω t)
F = ma = m
v (t ) = −Aω sin (ω t )
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a (t ) = −Aω 2 cos (ω t )
E = 12 kA2 = 12 kx2 + 12 mv2
k
1
2π
,ω=
, ω=
f = ,ω =
m
T
T
v = f λ, k =
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g
l
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vsound = €
344 m/s at 20 oC, vstring =
Ft
P
P
(for point source)
=
Area 4πr 2
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I
W
β = (10dB )log , where I 0 = 10 −12 2
I0
m
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2L
⎛ v ⎞
, f n = n⎜ ⎟, n = 1,2,3, …
λn =
n
⎝ 2L ⎠
4L
⎛ v ⎞
, f n = n⎜ ⎟, n = 1,3,5,…
λn =
n
⎝ 4L ⎠
f beat = f a − f b
double slit/grating: d sin θ = mλ (max)
v light = 3.0 ×10 8 m/s
single slit: asin θ = pλ (min)
sin θ ≈ tan θ, for small θ
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g=9.8m/s2
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M=−
s"
s
Q = nCP ΔT
W= (area under p-V curve)
ΔV > 0, W < 0
ΔV < 0, W > 0
pV = nRT = Nk B T
µ
D(x, t) = (2Asin kx)sin(ω t)
f0
, moving source
f± =
1  vs v
f± = (1± vO v) f0 , moving observer
I=
Q = ± ML
2π
1
2π
, f = ,ω =
λ
T
T
y(x, t) = A cos(kx − ω t) , moving to right
pfluid = psurface + ρgd
m
ρ=
V
Archimides principle: a fluid
exerts a buoyant force equal
to weight of displaced fluid.
ΔEtherm = Q + W
Q = McΔT Q = nCV ΔT
1 1 1
= +
f s s!
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nair=1.00
nwater=1.33
K avg = 32 k B T
(translation)
At equilibrium
T1f = T2f = Tf
Ideal gas:
Eth = 23 nRT = 23 NkBT
CV = 32 R , CP = 52 R
1N
2
mv rms
3V
3kBT
3RT
vrms =
=
m
M
p=
Wcycle= (area inside
€ pV curve)
Wout
Q
= 1− C
QH
QH
T
eCarnot = 1− C
TH
e=
QC
QC
=
Wout QH − QC
TC
COPCarnot =
TH − TC
COP =
M = nM mol
N = nN A
N A = 6.02 ×10 23 mol-1
T (K)=T (oC)+273
STP: T=0 oC and p=1 atm
patm = 1.01×10 5 Pa
Troom= 20 oC =293 K
kB = 1.38 ×10−23 J/K
R=8.31 J/(mol K)