Ch 15 covers wave motion — types of waves, wave equation, speed of waves, principle of superposition, standing waves on strings and in pipes, beats, and the Doppler effect.
Transverse: particles move perpendicular to wave direction (string, EM waves). Longitudinal: particles move parallel (sound). Wave equation: y = A sin(kx − ωt), where k = 2π/λ (wave number), ω = 2πf. Speed v = fλ = ω/k. Speed on string: v = √(T/μ) where T is tension, μ is linear mass density.
Superposition: when two waves overlap, displacement = algebraic sum. Standing waves: two identical waves travelling in opposite directions → fixed nodes (zero displacement) and antinodes (max displacement). String fixed at both ends: harmonics f_n = nv/2L. Open pipe: f_n = nv/2L (all harmonics). Closed pipe: f_n = nv/4L (odd harmonics only).
Beats: two waves of slightly different frequencies produce pulsating sound. Beat frequency = |f₁ − f₂|. Doppler effect: apparent change in frequency due to relative motion. Source approaching: frequency increases. Source receding: frequency decreases. General formula: f' = f(v ± v_o)/(v ∓ v_s). Applications: radar speed guns, medical ultrasound, redshift in astronomy.
Download: https://ncert.nic.in/textbook/pdf/keph207.pdf | Part II: https://ncert.nic.in/textbook/pdf/keph2ps.zip
A closed pipe has a node at the closed end and an antinode at the open end. The fundamental fits λ/4 into the pipe length. The next resonance requires 3λ/4 (3rd harmonic), then 5λ/4 (5th harmonic), etc. Only odd multiples of the fundamental frequency can fit the boundary conditions (node at one end, antinode at the other).
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