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PHYS*1130 FORMULA SHEET
Wavestraveling waves
( )kxtyx
2t
T
2yy oo =
= sinsin
f2 = fk
Tv ===
standing waves
( ) kxt2yy o sincos=
Simple Harmonic MotionThe restoring force
kxF =
spring pendulum
xm
k
dt
xd2
2
=
=
l
g
dt
d2
2
( )+= tcosAx ( )+= tcosmax
m
kf2 ==
l
gf2 ==
k
m2T =
g
l2T =
( )( )o
2max
max2
1cos12gv
coscos2glv
=
=
( ) 2mech22 kA
2
1E;xm
2
1xU ==
Damped motion
( ) = +
bx A exp t cos t
2m
2
2
4m
b
m
k=
critical damping km2b =
Acoustics
A
PI = =
2
PI
4r 222 f2I A=
=
10
o
IIL 10 log
I 212o W/m10I
=
Pt=E 12
ff =b
f
Doppler shiftMoving source and stationary objectSource
approaching Source receding
f
1 sv
v
=
af f
1 sv
v
=+
rf
Stationary source and moving objectApproaching object Receding
object
s
f 1v
v
= +
af fv
v
=
srf 1
Moving source and moving object
Optics and Light Absorption
v
cn=
=
sin
0.3567I expsin35.1
2211 sinnsinn =
21
2
L2
1
1L21 PPr
nn
r
nn
q
n
p
n+=
+
=+
pn
qnm
2
1=
in air only
q
1
p
1
f
1P +==
O
I
p
qm ==
100I
I%T
o
= clI
IlogA o10 ==
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Astronomical telescopeLength =f (objective) +f (eyepiece)
Galilean telescope
Length =f (objective) |f (eyepiece)|Angular magnification
= f (objective) / f (eyepiece)Angular magnification of a simple
magnifier
=25 / f where f is in cm
Modern Physics
hchfE ==
mv
h
p
h ==
=
L
xnsin
L
2 2P =
for a linear molecule
2
e
22
nL8m
hn
E =
Electricity
rr
qkqF
2
21
=
rr
kqE
2
=
EqF
=
r
kqV
=
r
qkqU 21
= U =qV
229 CNm109.0k = constantdielectricis
C101.6chargeelectronic19
= field)(uniformEdV = ( ) = 0loopV ( ) ( ) = outIinI
IRV = =i
iseries RR =i iparallel R
1
R
1
2/II pRMS = A/LR = VIRIR/VP22 ===
2
1
2
1
N
N
V
V= 2/VV pRMS =
Useful Information
1 = 10-10 m J s106.63 34=h kg109.1m 31e=
J101.6eV1 19= radians = 180 23A 106.02N =
kg101.66054amu1 27= kg10m 27proton= 673.1
amu007276.1=protonm amu000549.0=electronm
amu008665.1=neutronm 18
ms102.9979c
=
2r4sphereofareasurface = 1kgJ0.01rad1 =
r2circleofncecircumfere =
Densities: Air 1.3 kg m-3 Water 1000 kg m-3Velocity of sound: in
air 340 m/s in water 1550 m/sIndex of refraction of water
=1.33Index of refraction of air =1
Radioactivity
( )texpNNo
= /0.693T1/2
=
bpeff += bpeff T
1
T
1
T
1+=
Absorption of radiation
( )xexpII o = /0.693HVT =
m= -1-3 kgJNEt10x3.0D =
2mcE = WhfE k =
Radiation
T(K)
K)m( =
3
m102.9 ( ) t
soseTTTT
+=
( )4284 KWm105.672TI == ( 4241net TTI =
kB= 1.38 x 10-23 J/K04/12
