Waves Formulas PDF

# Waves ## General Form * **DK = 2π** * **Vw = ω/K** * **y = Asin(ωt - kn)** General form of wave ## Phase Difference * **Δφ = ±(Δω)t + k Δn** * **Δφ = k Δm** ## Particle Velocity and Wave Velocity * **dy/dt = Vp** * **dy/dm = slope of wave** * **dy/dz = Vw** * **Vp = -Vw(slope)** ## Differen...

# Waves ## General Form * **DK = 2π** * **Vw = ω/K** * **y = Asin(ωt - kn)** General form of wave ## Phase Difference * **Δφ = ±(Δω)t + k Δn** * **Δφ = k Δm** ## Particle Velocity and Wave Velocity * **dy/dt = Vp** * **dy/dm = slope of wave** * **dy/dz = Vw** * **Vp = -Vw(slope)** ## Differential Form of SHW * **d²y/dt² - Vw²d²y/dn² = 0** ## Power and Intensity * **Pmax = ± uVwA²ω²/2** * **I = A¹²ω²/2** * **I = ½SVwA²ω²** * **I = A²²ω²/I²** ## Speed of Transverse Wave on Stretched String * **V = √(T/µ)** where µ is the linear mass distribution ## Bulk Modulus * **B = -VΔP/ΔV** ## Newton's Formula * **Vs = √(Y/ρ)** ## Laplace Formula * **Vs = √(B/ρ) = √(YRT/M)** ## Longitudinal Velocity * **Vl = √(T/ρ)** * **Vl = √(B/ρ)** ## Potential Differences * **ΔP₀ = KΔB** * **ΔS₀ = KΔS** * **ΔP = - ΔP₀cos(ωt - kn)** * **ΔP = - ΔP₀sin(ωt - kn - π)** * **ΔP = - ΔS₀cos(ωt - kn)** ## Intensity Resultants * **JR = I₁ + I₂ + 2√I₁√I₂cosθ** * **If A₁ = A₂ then:** * **AR = 2Acos(θ/2) and JR = 4Tcos²(θ/2)** ## Interference * **Constructive Interference:** * **A = 2απ** * **θ = 2απ** * **Destructive Interference** * **θ = (2α-1)π** ## Intensity Resultants for Interference * **Imax = (√I₁ + √I₂)²** * **Imin = (√I₁ - √I₂)²** ## Amplitudes for Interference * **AR = A₁ + A₂** * **AR = A₁ - A₂** ## Path Differences for Interference * **If I₁ = I₂ then Imax = 4T and if I₁ = I₂ then JR = 0** * **Δn = nλ** * **Δn = (2n-1)λ/2** ## Wave Amplitude * **A = A₀/√r** for spherical waves * **A = A₀/√n** for cylindrical waves where n is a constant ## Loudness * **L(dB) = 10log₁₀(I/I₀)** where I₀ is a reference intensity * **L(dB) = 10log₁₀(I/I₀)** where I₀ is a reference intensity ## Other Equations * **V = 2πf** * **λ = v/f** * **v = fλ** * **C.I = (nλ)** * **D.I = (2n-1)λ** * **Δn = πλ** * **y = πλ₀** * **Δn = (2n-1)λ/2** * **y = (2n-1)λ₀/2** * **Band width = Δf = β** * **Δx = ±d/2** ## Reflection of Waves * **At a fixed end:** * **yR = -Asin(ωt + kn)** * **At a free end:** * **yR = Asin(ωt + kn)** ## Raver to Denser * **fi = fR = fT** * **yi = Aisin(ωt - kn)** * **yR = Aisin(ωt + kn)** ## Denser to Raver * **yi = Aisin(ωt - kn)** * **yR = -Aisin(ωt + kn)** ## Amplitude of Reflected Wave * **AR = RAi** * **AR = (V₂ - V₁/V₁ + V₂)Ai** where R is the reflection coefficient ## Amplitude of Transmitted Wave * **AT = (2V₁/(V₁+V₂))Ai**