Waves L6 Superposition & Interference of Waves CBSE 11 & 12 Physics + JEE Foundation скачать в хорошем качестве

Waves L6 Superposition & Interference of Waves CBSE 11 & 12 Physics + JEE Foundation

In this lecture (Waves L6, duration ≈49 min) we build the full superposition + interference toolkit for waves using sound. The same mathematics will be reused almost as‑it‑is later in wave optics (Young’s double slit, thin films, etc.). What’s covered: Principle of superposition (linear medium, small displacements) Superposition of pulses on a string (constructive & destructive overlap) Q1: Two travelling pulses – direction of motion, time of global cancellation, position of permanent node Q2: Adding two sine waves at a point (direct evaluation) Trig identity: (\sin\alpha + \sin(\alpha + \phi)) Q3: Two equal‑amplitude sine waves with phase shift – resultant amplitude & frequency Coherent sources & precise definition of interference Derivation of resultant amplitude: (R^2 = A_1^2 + A_2^2 + 2A_1A_2\cos\phi) Interference intensity formula: (I = I_1 + I_2 + 2\sqrt{I_1I_2}\cos\phi) Conditions for maxima & minima: (\phi = (2\pi/\lambda)\Delta x), (\Delta x = n\lambda), (\Delta x = (2n+1)\lambda/2) Equal-amplitude case: (I = I_0\cos^2(\phi/2)) Q4 & Q5: Numericals on intensity with unequal powers Path difference toolkit summarised Selected sound interference problems: two speakers, angular interference, semicircular tube Q9: Simple 1D geometry with two sources on a line (constant path difference outside) Quincke’s tube: concept, (\lambda = 2x,\ v = 2n_0x) Overview of Q10, Q11, Q12: Quincke numericals & first off‑axis minimum from two speakers Bridge to wave optics: same formulas for light interference Key formulas: Superposition (linear medium): (y = y_1 + y_2 + \dots) Phase–path: (\phi = \dfrac{2\pi}{\lambda}\Delta x) Resultant amplitude: (R^2 = A_1^2 + A_2^2 + 2A_1A_2\cos\phi) Intensity: (I = I_1 + I_2 + 2\sqrt{I_1I_2}\cos\phi) Maxima: (\Delta x = n\lambda), (\phi = 2n\pi) Minima: (\Delta x = (2n+1)\dfrac{\lambda}{2}), (\phi = (2n+1)\pi) Equal amplitudes: (I = I_0\cos^2(\phi/2)) Quincke (successive maxima): (\lambda = 2x,\ v = 2n_0x) Level: CBSE Class 11 & 12 Physics + JEE Instructor: Dr Kedar Pathak