the atlas of physics

Vrms voltage v_mpeak voltage Irms current i_mpeak current

v_{m} = \sqrt{2} \cdot V

i_{m} = \sqrt{2} \cdot I

νfrequency ωangular frequency Linductance Ccapacitance X_Linductive reactance X_Ccapacitive reactance V_Lvoltage across the inductor V_Cvoltage across the capacitor πpi Irms current

ω = 2 \cdot π \cdot ν

X_{L} = 2 \cdot π \cdot ν \cdot L

X_{C} = \frac{1}{2 \cdot π \cdot ν \cdot C}

V_{L} = I \cdot X_{L}

V_{C} = I \cdot X_{C}

Rresistance Ppower drawn Vrms voltage Irms current

P = \frac{V^{2}}{R}

V = I \cdot R

Rresistance Zimpedance Ppower drawn ν_rresonant frequency φphase angle ω_rresonant angular frequency X_Linductive reactance X_Ccapacitive reactance Vrms voltage Irms current πpi Linductance Ccapacitance

Z^{2} = R^{2} + {(X_{L} - X_{C})}^{2}

V = I \cdot Z

P = I^{2} \cdot R

φ = atan (\frac{X_{C} - X_{L}}{R})

ν_{r} = \frac{1}{2 \cdot π \cdot \sqrt{L \cdot C}}

ω_{r} = 2 \cdot π \cdot ν_{r}

Zatomic number Kkinetic energy dclosest approach kcoulomb constant eelementary charge

K = \frac{k \cdot 2 \cdot e \cdot Z \cdot e}{d}

mmass rorbit radius vorbital speed E_bbinding energy nquantum number Zatomic number Upotential energy Etotal energy E_pphoton energy νfrequency kcoulomb constant eelementary charge πpi hplancks constant

E_{b} = \frac{k \cdot e^{2}}{2 \cdot r}

\frac{m \cdot v^{2}}{r} = \frac{k \cdot e^{2}}{r^{2}}

v = \frac{2 \cdot π \cdot k \cdot Z \cdot e^{2}}{n \cdot h}

m \cdot v \cdot r = \frac{n \cdot h}{2 \cdot π}

U = \frac{- k \cdot e^{2}}{r}

E = \frac{- k \cdot e^{2}}{2 \cdot r}

E_{p} = h \cdot ν

Icurrent Across section ρdensity Mmolar mass nfree electrons v_ddrift speed llength of the conductor tdrift time N_Aavogadro constant eelementary charge

n = \frac{ρ \cdot N_{A}}{M}

I = n \cdot e \cdot A \cdot v_{d}

l = v_{d} \cdot t

Vvoltage Icurrent Rresistance llength of the conductor Across section ρresistivity

V = I \cdot R

R = \frac{ρ \cdot l}{A}

αtemperature coefficient R₀reference resistance T₀reference temperature Ttemperature Rresistance

R = R_{0} \cdot (1 + α \cdot (T - T_{0}))

mmass vspeed λde broglie wavelength hplancks constant

λ = \frac{h}{m \cdot v}

φ₀work function ν₀threshold frequency V₀stopping potential K_maxmaximum kinetic energy hplancks constant eelementary charge νfrequency

h \cdot ν_{0} = φ_{0}

e \cdot V_{0} = h \cdot ν - φ_{0}

e \cdot V_{0} = K_{\max}

νfrequency λwavelength Ephoton energy pphoton momentum Pemitted power Nphotons a second Vaccelerating potential hplancks constant cspeed of light

E = h \cdot ν

c = ν \cdot λ

p = \frac{h}{λ}

P = N \cdot E

rseparation F_eelectric force kcoulomb constant qcharge

F_{e} = \frac{k \cdot q_{1} \cdot q_{2}}{r^{2}}

qcharge nnumber of charges n_dotcharges a second tcharging time eelementary charge

q = n \cdot e

n = n_{dot} \cdot t

Efield strength rseparation E_qfield of a charge Fforce of the field qcharge kcoulomb constant

F = q \cdot E

E_{q} = \frac{k \cdot q}{r^{2}}

Efield strength Aarea rradius Φelectric flux qcharge inside Ddiameter σsurface charge density λlinear charge density E_lfield near a line E_pfield between plates πpi ε₀permittivity of free space

A = π \cdot r^{2}

Φ = E \cdot A

Φ = \frac{q}{ε_{0}}

A = π \cdot D^{2}

q = σ \cdot A

E_{l} = \frac{λ}{2 \cdot π \cdot ε_{0} \cdot r}

E_{p} = \frac{σ}{ε_{0}}

Bmagnetic field Nturns Aarea νfrequency ε₀peak emf πpi

ε_{0} = N \cdot B \cdot A \cdot 2 \cdot π \cdot ν

Nturns Aarea Rresistance Bmagnetic field θangle to the field Φmagnetic flux εinduced emf Iinduced current Δttime taken flux through a loop emf from the change of flux current driven by the emf Bmagnetic field Rlength of the rod ωangular speed εinduced emf

ε = \frac{B \cdot ω \cdot R^{2}}{2}

Eelectric field Bmagnetic field kwave number ωangular frequency λwavelength νfrequency cspeed of light πpi

E = c \cdot B

k = \frac{2 \cdot π}{λ}

ω = 2 \cdot π \cdot ν

c = ν \cdot λ

Ccapacitance Qcharge Vvoltage Uenergy stored Aarea dplate separation Kdielectric constant ε₀permittivity of free space

Q = C \cdot V

C = \frac{K \cdot ε_{0} \cdot A}{d}

U = \frac{C \cdot V^{2}}{2}

Efield strength pdipole moment θangle to the field Upotential energy Qheat given out qcharge llength of the dipole τtorque energy of a dipole in a field

p = q \cdot l

τ = p \cdot E \cdot \sin θ

energy lost as heat qcharge rdistance Vpotential Wwork to bring in kcoulomb constant

V = \frac{k \cdot q}{r}

W = q \cdot V

qcharge rdistance Upotential energy kcoulomb constant

U = \frac{k \cdot q_{1} \cdot q_{2}}{r}

Mcentral mass R_ccentral radius hheight of the orbit k_Kkeplers constant E_bbinding energy vspeed Ggravitational constant rradius πpi Tperiod mmass

v^{2} = \frac{G \cdot M}{r}

k_{K} = \frac{4 \cdot π^{2}}{G \cdot M}

T^{2} = k_{K} \cdot r^{3}

r = R_{c} + h

E_{b} = \frac{G \cdot M \cdot m}{2 \cdot r}

rdistance from the centre hheight above the surface V_ggravitational potential v_eescape speed vspeed Rradius of the body mmass height is measured from the surface potential of a mass escape speed from where it is energy kept in free flight mmass Rradius of the body g_ssurface gravity r_gseparation E_ggravitational intensity Ggravitational constant

g_{s} = \frac{G \cdot m}{R^{2}}

E_{g} = \frac{G \cdot m}{{r_{g}}^{2}}

Ppressure Vvolume namount Ttemperature Mmolar mass ρdensity Rgas constant

P \cdot V = n \cdot R \cdot T

ρ = \frac{n \cdot M}{V}

lmean free path ν_ccollision frequency Rgas constant Ttemperature πpi dmolecular diameter Ppressure N_Aavogadro constant v_rmsrms speed

l = \frac{R \cdot T}{\sqrt{2} \cdot π \cdot d^{2} \cdot P \cdot N_{A}}

ν_{c} = \frac{v_{rms}}{l}

dmolecular diameter rmolecular radius V_mvolume of the molecules f_Vfraction filled by molecules Nmolecules πpi Vvolume namount

d = 2 \cdot r

V_{m} = \frac{N \cdot π \cdot d^{3}}{6}

f_{V} = \frac{V_{m}}{V}

n \neq 0

mmass Nmolecules namount Mmolar mass N_Aavogadro constant

m = n \cdot M

N = n \cdot N_{A}

v_rmsrms speed E_avgaverage thermal energy Rgas constant Ttemperature Mmolar mass N_Aavogadro constant

v_{rms} = {(\frac{3 \cdot R \cdot T}{M})}^{0.5}

E_{avg} = \frac{3 \cdot R \cdot T}{2 \cdot N_{A}}

fdegrees of freedom C_vmolar heat at fixed volume ΔTtemperature rise Qheat at fixed volume Rgas constant namount

C_{v} = \frac{f \cdot R}{2}

Q = n \cdot C_{v} \cdot Δ T

pmomentum Jimpulse p₀starting momentum pfinal momentum mmass v₀starting velocity vfinal velocity F_netnet force Δttime taken

{\vec{p}}_{0} = m \cdot {\vec{v}}_{0}

\vec{p} = m \cdot \vec{v}

\vec{J} = \vec{p} - {\vec{p}}_{0}

\vec{J} = {\vec{F}}_{net} \cdot Δ t

mmass F_netnet force Fforce Wweight aacceleration ggravity

{\vec{F}}_{net} = m \cdot \vec{a}

m \neq 0

free of forces weight of a body net force is the resultant second law in size

μ_rrelative permeability Icurrent nturns per length Hmagnetic intensity Mmagnetisation Bmagnetic field I_mmagnetising current μ₀permeability of free space

H = n \cdot I

M = (μ_{r} - 1) \cdot H

B = μ_{r} \cdot μ_{0} \cdot H

B = μ_{0} \cdot n \cdot (I + I_{m})

dpiston diameter rpiston radius sstroke Vvolume pushed Aarea πpi

d = 2 \cdot r

A = \frac{π \cdot d^{2}}{4}

V = A \cdot s

mmass ggravity Fthrust Aarea Ppressure

P = \frac{F}{A}

P_apressure at the surface ρdensity hdepth P_ggauge pressure ggravity Ppressure

P_{g} = ρ \cdot g \cdot h

P = P_{a} + P_{g}

ggravity aradius ρdensity σdensity of the fluid v_tterminal velocity ηcoefficient of viscosity

v_{t} = \frac{2 \cdot a^{2} \cdot (ρ - σ) \cdot g}{9 \cdot η}

Ssurface tension rradius ΔPexcess pressure ΔP_sexcess pressure in a soap bubble P_ipressure inside lslider length F_Spull of the film Ppressure

Δ P = \frac{2 \cdot S}{r}

Δ P_s = \frac{4 \cdot S}{r}

P_{i} = P + Δ P

F_{S} = 2 \cdot S \cdot l

mmass ggravity Aarea lfilm thickness vspeed Fviscous drag ηcoefficient of viscosity

F = \frac{η \cdot A \cdot v}{l}

Bbulk modulus ΔV_Vfractional compression aedge Vvolume ΔVfall in volume ρ_Bdensity when squeezed P_ggauge pressure ρdensity

B = \frac{P_{g}}{Δ V_V}

V = a^{3}

Δ V_V = \frac{Δ V}{V}

ρ_{B} = \frac{ρ}{1 - Δ V_V}

mmass ggravity Fshearing force Aface l_faceface length w_faceface width Lheight Δxshift σ_sshearing stress θ_sshearing strain Gshear modulus

A = l_{face} \cdot w_{face}

σ_{s} = \frac{F}{A}

θ_{s} = \frac{Δ x}{L}

G = \frac{σ_{s}}{θ_{s}}

mmass ggravity Fload rthickness Ddiameter Across section Loriginal length ΔLextension σstress εstrain Yyoungs modulus πpi

r = \frac{D}{2}

A = π \cdot r^{2}

σ = \frac{F}{A}

ε = \frac{Δ L}{L}

Y = \frac{σ}{ε}

αdirection vvelocity

v_{x} = v \cdot \cos θ

ggravity aacceleration

a_{x} = 0

rradius vspeed ωangular speed n_revrevolutions νfrequency a_ccentripetal acceleration qagainst gravity Tperiod ggravity mmass F_ccentripetal force πpi Δttime taken

v = ω \cdot r

ω = 2 \cdot \frac{π}{T}

ν = \frac{1}{T}

ν = \frac{n_{rev}}{Δ t}

a_{c} = \frac{v^{2}}{r}

q = \frac{a_{c}}{g}

F_{c} = m \cdot a_{c}

volumevolume massmass speedspeed densitydensity nnumber of moles angular_frequencyangular frequency workwork currentcurrent temperaturetemperature pressurepressure timetime powerpower stotal path length energyenergy gravitational_potentialgravitational potential μcoefficient of friction chargecharge accelerationacceleration velocityvelocity displacementdisplacement angular_velocityangular velocity forceforce angular_momentumangular momentum p_linlinear momentum electric_fieldelectric field average_velocityaverage velocity magnetic_momentmagnetic moment v_ABrelative velocity impulseimpulse Afirst vector Bsecond vector φangle between Rresultant βresultant direction αdirection A_xx component A_yy component

R^{2} = A^{2} + B^{2} + 2 \cdot A \cdot B \cdot \cos φ

R \cdot \sin β = B \cdot \sin φ

R \cdot \cos β = A + B \cdot \cos φ

A_{x} = A \cdot \cos α

A_{y} = A \cdot \sin α

A = \sqrt{{A_{x}}^{2} + {A_{y}}^{2}}

vvelocity Δvchange of velocity a_avaverage acceleration v₀starting velocity vfinal velocity Δttime taken

{\vec{Δ}}_{v} = \vec{v} - {\vec{v}}_{0}

{\vec{a}}_{av} = \frac{{\vec{Δ}}_{v}}{Δ t}

vvelocity

v_{1} = v_{2} - v_{3}

aacceleration ggravity ttime vfinal velocity v₀starting velocity xfinal position x₀starting position

\vec{v} = {\vec{v}}_{0} + \vec{a} \cdot t

\vec{x} = {\vec{x}}_{0} + {\vec{v}}_{0} \cdot t + \frac{\vec{a} \cdot t^{2}}{2}

{\vec{v}}^{2} = {\vec{v}}_{0}^{2} + 2 \cdot \vec{a} \cdot (\vec{x} - {\vec{x}}_{0})

\vec{x} - {\vec{x}}_{0} = \frac{(\vec{v} + {\vec{v}}_{0}) \cdot t}{2}

a_{1} = a_{2}

xposition Δxdisplacement dpath length Δttime taken v_avaverage velocity c_avaverage speed x₀starting position xfinal position

{\vec{Δ}}_{x} = \vec{x} - {\vec{x}}_{0}

{\vec{v}}_{av} = \frac{{\vec{Δ}}_{x}}{Δ t}

c_{av} = \frac{d}{Δ t}

d_{1} = d_{2} + d_{3}

Δ t_{1} = Δ t_{2} + Δ t_{3}

Bmagnetic field Icurrent Nturns Rradius Aarea mmagnetic moment θangle to the field τtorque πpi

m = N \cdot I \cdot π \cdot R^{2}

m = N \cdot I \cdot A

τ = m \cdot B \cdot \sin θ

Icurrent Nturns Rradius Llength of the coil nturns per length B_cfield at the centre B_sfield inside ddistance from the wire B_wfield near a wire μ₀permeability of free space πpi

B_{c} = \frac{μ_{0} \cdot N \cdot I}{2 \cdot R}

n = \frac{N}{L}

B_{w} = \frac{μ_{0} \cdot I}{2 \cdot π \cdot d}

B_{s} = μ_{0} \cdot n \cdot I

ggravity Bmagnetic field mmass qcharge vspeed Icurrent llength in the field Fforce on a wire fforce per length rradius of the path θangle to the field νfrequency of revolution πpi

F = I \cdot l \cdot B

f = I \cdot B \cdot \sin θ

r = \frac{m \cdot v}{q \cdot B}

v = 2 \cdot π \cdot r \cdot ν

m_Hhydrogen atom mass m_nneutron mass mmass Eenergy Zatomic number Amass number dmmass defect E_bbinding energy Qq value cspeed of light

E = m \cdot c^{2}

dm = Z \cdot m_{H} + (A - Z) \cdot m_{n} - m

E_{b} = dm \cdot c^{2}

Q = dm \cdot c^{2}

R₀size of a nucleon s share Amass number Zatomic number mmass Rnuclear radius ρnuclear density U_bcoulomb barrier πpi kcoulomb constant eelementary charge

R = R_{0} \cdot A^{0.333333333}

ρ = \frac{m}{\frac{4 \cdot π \cdot R^{3}}{3}}

U_{b} = \frac{k \cdot {(Z \cdot e)}^{2}}{2 \cdot R}

Nrepetitions νfrequency Tperiod Δttime taken

ν = \frac{N}{Δ t}

T = \frac{1}{ν}

Aamplitude sstroke ωangular frequency νfrequency φphase constant v_maxmaximum speed a_maxmaximum acceleration aacceleration πpi xposition Δttime taken vvelocity

s = 2 \cdot A

ω = 2 \cdot π \cdot ν

v_{\max} = ω \cdot A

a_{\max} = ω^{2} \cdot A

displacement in shm velocity in shm acceleration in shm amplitude from where and how fast gsurface gravity Llength of the string Tperiod πpi

T = 2 \cdot π \cdot \sqrt{\frac{L}{g}}

mmass kspring constant Kkinetic energy Upotential energy Etotal energy ωangular frequency Aamplitude vvelocity xposition

ω^{2} = \frac{k}{m}

E = \frac{k \cdot A^{2}}{2}

energies at an instant

r_sreflectance s polarised r_preflectance p polarised rreflectance τtransmittance μ₁refractive index of first medium iangle of incidence μ₂refractive index of second medium r_rangle of refraction

r_{s} = {(\frac{μ_{1} \cdot \cos i - μ_{2} \cdot \cos r_{r}}{μ_{1} \cdot \cos i + μ_{2} \cdot \cos r_{r}})}^{2}

r_{p} = {(\frac{μ_{1} \cdot \cos r_{r} - μ_{2} \cdot \cos i}{μ_{1} \cdot \cos r_{r} + μ_{2} \cdot \cos i})}^{2}

r = \frac{r_{s} + r_{p}}{2}

r + τ = 1

r_langle of reflection iangle of incidence

i = r_{l}

μrefractive index r_rangle of refraction μ₁refractive index of first medium μ₂refractive index of second medium ccritical angle iangle of incidence

μ_{1} \cdot \sin i = μ_{2} \cdot \sin r_{r}

μ_{1} \cdot \sin c = μ_{2} \cdot \sin 90 °

r_{r} = 90 °

i > c

r_{r} < i

r_{r} > i

n₁index before n₂index after Rradius of curvature uobject distance d_odistance in front vimage distance

u = - d_{o}

\frac{n_{2}}{v} - \frac{n_{1}}{u} = \frac{n_{2} - n_{1}}{R}

μ₂₁relative refractive index μ₂refractive index of second medium μ₁refractive index of first medium

μ_{21} = \frac{μ_{2}}{μ_{1}}

Rradius of curvature r_sizesize of the radius d_odistance in front ffocal length f_sizesize of the focal length uobject distance vimage distance mmagnification h_oobject height h_iimage height

u = - d_{o}

f = \frac{R}{2}

\frac{1}{v} + \frac{1}{u} = \frac{1}{f}

m = \frac{- v}{u}

m = \frac{h_{i}}{h_{o}}

nrefractive index of the lens n_sindex of the surroundings R₁first radius R₂second radius r₂size of the second radius ffocal length f_sizesize of the focal length Ppower of the lens d_odistance in front uobject distance vimage distance mmagnification h_oobject height h_iimage height

u = - d_{o}

\frac{1}{f} = (\frac{n}{n_{s}} - 1) \cdot (\frac{1}{R_{1}} - \frac{1}{R_{2}})

P = \frac{1}{f}

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

m = \frac{v}{u}

m = \frac{h_{i}}{h_{o}}

rreflectance

r = 1

n_iintrinsic carriers n_aatoms x_ddoping N_Ddonors n_eelectrons n_hholes

N_{D} = x_{d} \cdot n_{a}

n_{e} = N_{D}

n_{e} \cdot n_{h} = {n_{i}}^{2}

Mmass Rradius Imoment of inertia Fpull τtorque lcord unwound K_rotrotational kinetic energy Langular momentum α_rangular acceleration θangle turned ωangular velocity

I = \frac{M \cdot R^{2}}{2}

τ = I \cdot α_{r}

l = R \cdot θ

torque of a pull at the rim kinetic energy of turning angular momentum of turning ωangular velocity α_rangular acceleration θangle turned n_revturns ω₀starting angular velocity ωfinal angular velocity Δttime taken πpi

ω = ω_{0} + α_{r} \cdot Δ t

θ = ω_{0} \cdot Δ t + \frac{α_{r} \cdot {Δ t}^{2}}{2}

ω^{2} = {ω_{0}}^{2} + 2 \cdot α_{r} \cdot θ

n_{rev} = \frac{θ}{2 \cdot π}

mmass sspecific heat capacity Llatent heat T₁temperature at first T₂temperature after Qheat to warm Q_Lheat to change phase Q_inheat taken in

Q = m \cdot s \cdot (T_{2} - T_{1})

Q_{L} = m \cdot L

Q_{in} = Q + Q_{L}

Kthermal conductivity Across section Llength of the rod T_Chot end T_Dcold end Hheat current

H = \frac{K \cdot A \cdot (T_{C} - T_{D})}{L}

Ttemperature k_ccooling constant T₀starting temperature T_ffinal temperature Δttime taken

\frac{T_{1} - T_{2}}{Δ t} = - k_{c} \cdot (\frac{T_{2} + T_{1}}{2} - T_{3})

L₁length at first L₂length after Δlchange in length T₁temperature at first T₂temperature after α_lcoefficient of linear expansion

L_{2} - L_{1} = α_{l} \cdot L_{1} \cdot (T_{2} - T_{1})

Δ l = L_{2} - L_{1}

Ppressure Vvolume γratio of specific heats P₁starting pressure P₂final pressure V₁starting volume V₂final volume

P_{1} \cdot {V_{1}}^{γ} = P_{2} \cdot {V_{2}}^{γ}

ΔQheat absorbed ΔWwork done by the system W_onwork done on the system ΔUchange of internal energy

Δ Q = Δ U + Δ W

W_{on} = - Δ W

llength ggravity mmass Tperiod kconstant xpower of length ypower of gravity zpower of mass vspeed hheight ttime aacceleration s₀start v₀starting speed sdistance m₀rest mass Kkinetic energy

T = k \cdot l^{x} \cdot g^{y} \cdot m^{z}

x + y = 0

-2 \cdot y = 1

z = 0

\frac{m \cdot v^{2}}{2} = m \cdot g \cdot h

s = s_{0} + v_{0} \cdot t + \frac{a \cdot t^{2}}{2}

Vvolume vspeed aacceleration Fforce ρdensity Wwork Ssurface area hheight bbreadth S_ccylinder surface area V_svolume of a slab ρ_relrelative density ρ_wdensity of water m_llinear magnification l_iimage length l_oobject length A_iimage area A_oobject area V_Nvolume of them all V_mmolar volume R_Vroom to spare llength ttime mmass πpi rradius Aarea Nnumber of entities

V = l^{3}

v = \frac{l}{t}

a = \frac{v}{t}

F = m \cdot a

ρ = \frac{m}{V}

W = F \cdot l

S = 6 \cdot l^{2}

V = \frac{4 \cdot π \cdot r^{3}}{3}

S_{c} = 2 \cdot π \cdot r \cdot (r + h)

A = l \cdot b

V_{s} = l \cdot b \cdot h

ρ_{rel} = \frac{ρ}{ρ_{w}}

m_{l} = \frac{l_{i}}{l_{o}}

{m_{l}}^{2} = \frac{A_{i}}{A_{o}}

V_{N} = N \cdot V

R_{V} = \frac{V_{m}}{V_{N}}

πpi cspeed of light hplancks constant eelementary charge Ggravitational constant kcoulomb constant ε₀permittivity of free space μ₀permeability of free space Rgas constant N_Aavogadro constant afirst measured Δaerror in first δ_arelative error in first bsecond measured Δberror in second δ_brelative error in second pproduct Δperror in product δ_prelative error in product ttotal ddifference l_cleast count d_mscale division N_ddivisions read past

δ_{a} = \frac{Δ a}{a}

δ_{b} = \frac{Δ b}{b}

p = a \cdot b

δ_{p} = δ_{a} + δ_{b}

Δ p = δ_{p} \cdot p

t = a + b

d = a - b

l_{c} = \frac{d_{m}}{N_{d}}

llength mmass ttime Ielectric current Ttemperature namount of substance I_vluminous intensity sarc length rradius θplane angle Aarea Ωsolid angle t_lightlight time d_lightlight distance Nnumber of entities Bbaseline Ddistance away θ_pparallax angle cspeed of light N_Aavogadro constant

θ = \frac{s}{r}

Ω = \frac{A}{r^{2}}

d_{light} = c \cdot t_{light}

N = n \cdot N_{A}

θ_{p} = \frac{B}{D}

θangle to the light s polarisation tshare passed

t = {\cos θ}^{2}

νfrequency ν_beatbeat frequency

ν_{beat} = ν_{1} - ν_{2}

vspeed of sound Llength of the pipe nharmonic νfrequency

ν = \frac{n \cdot v}{4 \cdot L}

Ppressure Ttemperature Mmolar mass ρdensity γratio of specific heats vspeed of sound Rgas constant

ρ = \frac{P \cdot M}{R \cdot T}

v = \sqrt{\frac{γ \cdot P}{ρ}}

vspeed of sound Llength of the pipe nharmonic νfrequency

ν = \frac{n \cdot v}{2 \cdot L}

aamplitude kwave number ωangular frequency λwavelength Tperiod νfrequency vwave speed Δxseparation Δφphase difference πpi

k = \frac{2 \cdot π}{λ}

ω = \frac{2 \cdot π}{T}

ν = \frac{1}{T}

v = ν \cdot λ

Δ φ = k \cdot Δ x

mmass Llength of the string μlinear mass density Ttension vwave speed ttravel time nharmonic νfrequency kwave number ωangular frequency

μ = \frac{m}{L}

v = \sqrt{\frac{T}{μ}}

v = \frac{ω}{k}

t = \frac{L}{v}

ν = \frac{n \cdot v}{2 \cdot L}

Kkinetic energy ΔKchange of kinetic energy mmass vvelocity F_netnet force Fforce Wweight W_Fwork W_gwork by gravity kinetic energy of a body kinetic energy gained work energy theorem Ppower F_netnet force Fforce Wweight vvelocity power of a force W_Fwork W_gwork by gravity W_netnet work F_netnet force Fforce Wweight Δxdisplacement work of a steady force work of the net force work of the weight

The atlas of physics 94 laws · 382 quantities · 299 equations