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Wave Formula

Electromagnetic wave equations are given as below

DescriptionFormula
Gauss’s Law for electricity∮ E.da=Q/ϵ_0
Gauss’s Law for MagnetismB.dA=0
Faraday’s LawE.dl=-dϕdt
Ampere-Maxwell Law∮ B.dl=μ_0 ϵ_0 (dϕ_E)/dt
Speed of Light in Vacuumc=1/√(μ_0 ϵ_o )
Speed of light in mediumv=1/√μϵ
Relation between Electric and Magnetic fieldE_0/B_0 =c

Wave Formula

The formula for wave  are as stated below

DescriptionFormula
General Equation of Wave Motion(∂^2 y)/(∂t^2 )=v^2 (∂^2 y)/(∂x^2 )
Wave number
Phase of a Wave

It is the difference in phases of two particles at any time t.

∆ϕ=2π/λ∆x  

Speed of Transverse Wave Along a String / Wirev=√(T/μ) where T=Tension(-1)

μ=mass per unit length

Power Transmitted Along The String By a Sine Wave

Average Power (P)

P=2π^2 f^2 A^2 μv v =velocity

Intensity

I=P/S=2π^2 f^2 A^2 ρv
Longitudinal Displacement of Sound Waveϵ=A sin⁡(ωt-kx)
Pressure Excess during travelling sound waveP_ex=-B ∂ϵ/∂x=(B) Cos (ωt-kx)

Where B is the Bulk Modulus

Pex is the excess pressure

Speed of Sound C=√(E/ρ)

Here, E is elastic modulus ρ

is the density of medium

Loudness of Sound 10 ( I/I_0 ) dB
Intensity at a distance r from a point SourceI=P/(4πr^2 )
Interference of Sound WaveP_1=P_m1 Sin(ωt-kx_1+θ_1 ) P_2=P_m2 Sin(ωt-kx_2+θ_2)The Result is the sum of all the pressure. P_0=√(p_(m_1)^2+p_(m_2)^2+2p_(m_1 ) P_m2 cosϕ)
For constructive Interferenceϕ=2πn then,=>P_o=P_(m_1 )+P_(m_2 )
For destructive interferenceϕ=(2n+1)π and=>P_o=|P_(m_1 )-P_(m_2 ) |
Close Organ Pipef=v/4l,3v/4l,5v/4l,….((2n+1)v)/4l
Open organ pipef=v/2l,2v/2l,…nV/2l
BeatsBeats Frequency=f1–f2
Doppler’s Law

The Observed Frequency,

f^'=f((v-v_0)/(v-v_s ))

Apparent Wavelength,

λ^'=λ((v-v_s)/v)

Wave Optics Formula

The formula for wave optics are as stated below

DescriptionFormulas
The path difference of two coherent Waves

∆d=d2–d1

∆d is the path difference

The Path difference of two coherent waves: Interference Maximum

∆d=k.λ

∆d is path difference λ

is the wavelength

The path difference of two coherent waves: Interference Minimum∆d=((2.k+1).λ)/2

∆d is path difference λ

is the wave length

Thin-film interference: Constructive (maximum)2ntcos r =(n+1/2)λ

t is film thickness

n is refractive index

r is refraction angle

λ is wave length

Thin-Film interference: destructive (minimum)2ntcosr =nλ

t is film thickness

n is refractive index

r is refraction angle

λ is wave length

Radii of Newton’s Ring

 r=√(k.R.λ)    or    r=√(((2.k+1).R.λ) )/2

r is the radius

R is the radius of curvature

λ is the wavelength

Light Diffractionl=d^2/(4.λ)

I is the distance from obstacle

d is the obstacle size

λ is wavelength

Diffraction grating: maximum (bright stripes)dsinθ =kλ

d is the lattice constant

is the diffraction angle

λ is the wavelength

Diffraction grating (dark stripes)dsinθ =(K+1/2)λ

d is the lattice constant

is the diffraction angle

λ is the wavelength

Work Power and Energy Formula

The formula for work power energy are as stated below

DescriptionFormulas
Work done is given by

W=F×d

F is the force

d is the displacement

Kinetic EnergyK.E=1/2 mv^2

m is the mass of the body.

v is the velocity of the body

Potential Energy

P.E=mgh

m is the mass of the body in kg

h is the height of the body in meters

g is the  acceleration due to gravity

Power

P=W/t

W is the work done by the body

t is the time

P=(F ⃗.(ds) ⃗)/dt=F ⃗.V ⃗
Conservative ForcesF=-du/dr
Work-Energy theoremW_net=∆K

Where

Wnet is the sum of all forces acting on the object

K is the change of kinetic energy

Kinetic Theory Formula

The formula for kinetic theory are as stated below

DescriptionFormula
Boltzmann’s Constantk_B= nR/N

kB = Boltzmann’s constant

R = gas constant

n = number of moles

N = number of particles in one mole 

Total translational Kinetic Energy of GasK.E = 3/2 (nRT)

R = gas constant

n = number of moles

T = absolute temperature

Maxwell distribution law

V_rms>V>V_p

V_rms
= RMS speed

Vp = most probable speed

V = average speed

RMS SpeedV_rms= √(3kt/m) = √(3Rt/M)

R = universal gas constant

T = absolute temperature

M = molar mass

Average Speedv ⃗=√(8kt/πm) = √(8Rt/πM)
Most probable speedv_p=√(2kt/m) = √(2Rt/M)
Pressure of ideal gasp = 1/3 ρ〖v^2〗_rms
Equipartition of energy

For each degree of freedom

K=1/2 k_B T

For f degree of freedom

K=f/2 k_B T

kB = Boltzmann’s constant

T = temperature of gas

Internal Energy

For n moles of an ideal gas, internal energy is given as

U=f/2 (nRT)

Kinetic Theory of Gases Formula

The formula for kinetic theory of gases are as stated below

DescriptionFormulas
Boltzmann’s Constantk_B=nR/N
  •  k_Bis the Boltzmann’s Constant
  • R is the gas Constant
  • n is the Number of Moles
  • N is the Number of Particles in one mole (the Avogadro number)
Total Translational K.E of GasK.E=(3/2)nRT
  • n is the number of moles
  • R is the Universal gas Constant
  • T is the absolute Temperature
Maxwell Distribution LawV_rms>V>Vp
  • V_rms is the RMS speed
  • V is the Average Speed.
  • Vp is the most probable speed
RMS Speed (Vrms)V_rms=√(8kt/m)=√(3RT/M)
  • R is the universal gas constant.
  • T is the absolute temperature.
  • M is the molar mass.
Average Speedv ⃗=√(8kt/πm)=√(8RT/πM)
Most Probable Speed (Vp )V_p=√(2kt/m)=√(2RT/M)
The Pressure of Ideal GasP=1/3 V_rms^2
  • P is the density of molecules
Equipartition of Energy

 K=1/2 K_B T  for each degree of freedom

 K=(f/2) K_B T
for molecules having f degrees of freedom

  • KB is the Boltzmann’s Constant
  • T is the Temperature of the gas
Internal EnergyU=(f/2)nRT
  • For n moles of an ideal Gas.

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