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Category: Architectural Acoustics

$A\propto S\Rightarrow A=aS\Rightarrow a=\frac{A}{S}$Description: The sound absorption coefficient a describes the property of a material to convert incident sound into other forms of energy - e.g. Thermal or Kinetic Energy; and thus to absorb it. Where, A = total equivalent sound absorbing area & S = total sound energy incident on it.

Category: Architectural Acoustics

$CO=DepthofSea=\frac{vt}{2}$Description: Related to SONAR

Category: Architectural Acoustics

$d=\frac{{\lambda}_{u}}{2},{\lambda}_{u}=Wavelengthofultrasonicwave$Description: The distance between adjacent nodal planes

Category: Architectural Acoustics

${I}_{L}=K\mathrm{log}\left(\frac{I}{{I}_{0}}\right)$Description: If K=1, then Intensity Level is expressed in a unit called "bel".

Category: Architectural Acoustics

$I=\frac{Q}{At}=2{\mathrm{\pi}}^{2}{\mathrm{f}}^{2}{\mathrm{a}}^{2}\mathrm{\rho v}$Description: Amount of Sound Energy(Q) flowing per unit area. Where, t=time, a=amplitude, f=frequency, v=velocity, ρ=density of medium.

Category: Architectural Acoustics

$L=K{\mathrm{log}}_{10}I$Description: Where, K = Constant. Note that Loudness is a physiological quantity. Equation is known as Weber-Fechner law.

Category: Architectural Acoustics

$T=\frac{0.167V}{\sum aS}$Description: where, V = Volume of hall, a = absorption coefficient, S = Surface area.

Category: Architectural Acoustics

$E=\frac{{E}_{m}}{{10}^{6}}att=T$Description: Sabine defined the reverberation time as the time taken by the sound intensity to fall to one millionth of its original intensity after the source stopped emitting sound.

Category: Architectural Acoustics

$\frac{dL}{dI}=\frac{K}{I}$Description: Decreases with increase in intensity.

Category: Architectural Acoustics

$v=f{\lambda}_{u}$Description: where, f = frequency of ultrasonic wave

Category: Architectural Acoustics

${\lambda}_{u}=\frac{2n\lambda}{\mathrm{sin}\theta}$Description: where, θ is the angle of diffraction for the nth -order principle maxima

Category: Dielectrics

$\mu =q\times x$Description: A pair of equal and opposite charges separated by a small distance(x) constitutes an electric dipole.

Category: Dielectrics

$D={\in}_{\circ}E+P$Description: Relation between Flux Density & Polarization.

Category: Dielectrics

$E=\frac{F}{q}=\frac{kq}{{r}^{2}}$Description: Force that acts on a unit positive charge at a point.

Category: Dielectrics

$E=\frac{F}{q}$Description: Force per charge. Where, F = force & q = charge. Units are Newton/Coulomb or N/C.

Category: Dielectrics

$\varphi =EA\mathrm{cos}\theta $Description: Total number of electric field lines passing a given area in a unit time. Flux is Scalar. Where, E = Electric field & A = Area.

Category: Dielectrics

$D=\frac{\Phi}{A}$Description: Flux per unit area.

Category: Dielectrics

${\alpha}_{e}=\frac{{\in}_{0}\left({\in}_{r}-1\right)}{N}=4\mathrm{\pi}{\in}_{0}{\mathrm{R}}^{3}$Description: Due to the presence of Electron. Obtained in Solids. Independent of Temperature. Where, N is Number of atoms per unit Volume.

Category: Dielectrics

${\chi}_{e}={\in}_{r}-1$Description: Ratio of Polarization to net electric field as modified by the induced charges on the surface of the dielectric. It' s Unit-less.

Category: Dielectrics

$V=\frac{kq}{r},\left(k\left(cons\mathrm{tan}t\right)=1/4\mathrm{\pi}{\in}_{0}\right)$Description: Determines the direction of charge flow between two conducting bodies when brought in contact. Where, Potential Energy can considered as U = qV.

Category: Dielectrics

$P=N\mu $Description: Where, N = no. of electrons & µ = dipole moment

Category: Dielectrics

$F=k\frac{{q}_{1}{q}_{2}}{{r}^{2}}$Description: where, r = distance between the center of two charges.

Category: Dielectrics

${\in}_{\circ}k\int E\xb7ds=q$Description: For parallel plate capacitors.

Category: Dielectrics

$\frac{{q}_{1}{q}_{2}}{4\mathrm{\pi}{\in}_{\circ}}=\frac{{\mu}_{\circ}Idl*r}{4{\mathrm{\pi r}}^{{2}^{}}}\Rightarrow {\mu}_{\circ}\propto \frac{1}{{\in}_{\circ}}$Description: Ratio Between Electrical Induction & Dielectric Displacement Vector.

Category: Dielectrics

${\alpha}_{i}=\frac{{e}^{2}}{{{\omega}^{2}}_{\circ}}\left[\frac{1}{m}+\frac{1}{M}\right]$Description: Due to pressure of ions. Independent of Temperature. Where, ω = Natural Angular Frequency, m = Mass of anion, M = Mass of Cation.

Category: Dielectrics

$P={P}_{e}+{P}_{i}+{P}_{o}+0(PolrizabilityforAir)\Rightarrow P=N\alpha {E}_{int}$Description: Relation between all type of Polarizations.

Category: Dielectrics

$\lambda =\frac{q}{l}$Description: Charge per unit Length.

Category: Dielectrics

$R={R}_{\circ}\left[1+\alpha \left(t-{t}_{\circ}\right)\right]$Description: Materials in which the Dielectric Polarization is linearly related to the electric field & the dielectric constant is not dependent on electric field. Where, α is Temperature Constant.

Category: Dielectrics

${E}_{i}=E+\frac{p}{3{\in}_{0}}$Description: Total internal field for Dielectric.

Category: Dielectrics

(Number of atoms per unit cell * Number of electrons per atom) / volume of unit cellDescription: Unit : electrons/m^3

Category: Dielectrics

${\alpha}_{o}=\frac{{{\mu}^{2}}_{p}}{3{k}_{B}T}$Description: Due to Orientation in a particular direction. Dependent on Temperature. Where, kB is Boltzman Constant.

Category: Dielectrics

$\mu \propto E\Rightarrow \mu =\alpha E\Rightarrow \alpha \left(Polarizability\right)=\frac{\mu}{E}$Description: Polarizability Constant known itself as Polarizability.

Category: Dielectrics

$P\left(\overline{)r}\right)=\frac{\sum {P}_{n}}{\u2206v},\left({P}_{n}=DipoleMoment,v=volume\right)$Description: An average dipole moment, per unit volume, called the Polarization Vector P (r ).

Category: Dielectrics

${\in}_{r}=K=\frac{\in}{{\in}_{\circ}}$Description: Ratio : Permittivity of the medium / Permittivity of free space. Must be >>1.

Category: Dielectrics

$\sigma =\frac{q}{A}$Description: Charge per unit Area.

Category: Dielectrics

$\delta =\frac{q}{V}$Description: Charge per unit Volume.

Category: Dielectrics

$W=\frac{1}{2}{\in}_{\circ}V\left({\in}_{r}-1\right){E}^{2}$Description: Energy stored in Dielectric field.

Category: Fiber Optics

$\alpha ={\mathrm{sin}}^{-1}\left(\sqrt{{{n}^{2}}_{core}-{{n}^{2}}_{cladding}}\right)$Description: Maximum angle of the ray(against the fiber axis), hitting the fiber core which allows the incident light to be guided by the core.

Category: Fiber Optics

${\Theta}_{critical}={\mathrm{sin}}^{-1}\left(\frac{{n}_{r}}{{n}_{i}}\right),\left({n}_{r}=Refractivemedium,{n}_{i}=Incidentmedium\right)$Description: Angle is defined as the angle of incidence that provides an angle of refraction of 90-degrees

Category: Fiber Optics

$NA=\left(\sqrt{{{n}^{2}}_{core}-{{n}^{2}}_{cladding}}\right)$Description: It's the sign value of the Acceptance angle. It's the light gathering ability of the fiber.

Category: Laser

$E=hf=\frac{hc}{\lambda}$Description: where, h = plank constant(6.63*10^-34JS), c = Speed of light, λ = wavelength, f = frequency

Category: Laser

$\frac{{N}_{2}}{{N}_{1}}={e}^{\left(\frac{-\u2206E}{{K}_{B}T}\right)}$Description: where, Kb = Boltzman Constant

Category: Laser

${R}_{12}\propto {B}_{12}{N}_{1}\rho $Description: Where, ρ=density of incident radiation, B12 = probability of absorption of radiation per unit time, N1 = population of the lower energy level.

Category: Laser

${R}_{sp}={A}_{21}{N}_{2}$Description: where, A21 = probability of spontaneous emission per unit time, N2 = population at higher energy level E2

Category: Laser

${R}_{21\left(st\right)}={B}_{21}{N}_{2}\rho $Description: where, B21 = probability of stimulated emission per unit time, ρ = density of incident radiation, N2 = population of higher energy level E2

Category: Magnetic Materials

$\mu ={\mu}_{0}{\mu}_{r}$Description: µ of a medium is defined as the ability of the medium to allow the Magnetic Flux to penetrate through itself. Unit : H/m

Category: Magnetic Materials

${\mu}_{B}=\frac{e\overline{)h}}{2{m}_{e}},(\overline{)h}=1.055*{10}^{-34},{m}_{e}=Massofelectron,e=chargeofelectron)$Description: Value = 9.2771*10^-24. Smallest Unit of Magnetic Dipole Moment.

Category: Magnetic Materials

$H=\frac{F}{m}$Description: It's a measure of the force experienced by an unit north pole when placed at a point in magnetic field. where, F = force, m = strength of one pole.

Category: Magnetic Materials

$\varphi =BA$Description: It's the total number of lines of force emanating from the north pole of Magnet. where, B = Magnetic Induction, A = Area.

Category: Magnetic Materials

$B=\frac{\theta}{A}$Description: Magnetic flux passing through an unit area of cross section at that point. Unit : Tesla(T)

Category: Magnetic Materials

${\mu}_{m}=m\times l$Description: It's the measure of strength of the Magnet. where, m = strength of one of the pole, l = magnetic length in meter

Category: Magnetic Materials

${\chi}_{m}=\frac{M}{H}$Description: Shows how easily a substance can be magnetized. Unit-less. When (-ve) , solid is diamagnetic, high range - ferromagnetic, low range - paramagnetic

Category: Magnetic Materials

$M=\frac{MagneticMoment}{Volume}$Description: Pole strength acquired per unit area of cross section of the specimen.

Category: Magnetic Materials

${\mu}_{0}=\mu =\frac{B}{H}$Description: Ratio of Magnetic Induction B to the applied field H.

Category: Magnetic Materials

$B={\mu}_{0}\left(H+M\right)or\mu ={\mu}_{0}\left(1+\chi \right)or{\mu}_{r}=1+\chi $Description: Common relation among B, H, M, µ and χ

Category: Magnetic Materials

${\mu}_{r}=\frac{\mu}{{\mu}_{0}}\Rightarrow B={\mu}_{0}{\mu}_{r}H$Description: Permeability of any given medium is accessed relative to permeability of vacuum.

Category: Nanophysics

$Circumferenceoftube=\sqrt{3}d\xb7\sqrt{\left({a}^{2}+ab+{b}^{2}\right)}$Description: where, d = distance between two nearest carbon atoms, a & b are the chiral lengths.

Category: Nanophysics

$D=\frac{Circumferenceofthetube}{\mathrm{\pi}}$Description: Used for Carbon Nanotube

Category: Nanophysics

$SA:V=\frac{4{\mathrm{\pi r}}^{2}}{{\displaystyle \frac{4}{3}}{\mathrm{\pi r}}^{3}}=\frac{3}{r}$Description: where, r = radious

Category: Superconductivity

${I}_{c}=2{\mathrm{\pi rH}}_{\mathrm{c}}$Description: Maximum current amount that destroys the superconducting property. It depends on the size of superconductor.

Category: Superconductivity

${J}_{c}={I}_{c}/A$Description: Current Density corresponding to Critical Magnetic Field.

Category: Superconductivity

${H}_{c}={H}_{0}\left[1-{\left(\frac{T}{{T}_{c}}\right)}^{2}\right]$Description: The minimum magnetic field required to destroy the superconducting state.

Category: Superconductivity

$\nu \left(Nu\right)=\frac{2eV}{h}$Description: where, V = Potential Difference, h = Planck's Constant

Category: Superconductivity

${T}_{c}\propto 1/\sqrt{M}$Description: "The transition temperature is inversely proportional to the square root of isotopic mass of single superconductor"

Category: Ultrasonics

$f=\frac{1}{2\mathrm{\pi}\sqrt{\mathrm{LC}}}=\frac{1}{2l}\sqrt{\frac{E}{\rho}}$Description: LC represents Resonant Circuit. where, l = length of rod, E = elastic constant of rod, ρ = density

Category: Ultrasonics

$f=\frac{p}{2l}\sqrt{\frac{E}{\rho}}$Description: Same as the frequency of vibration of rod but here, p = Young's Modulus

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