Comprehensive notes for Chapter 7 Waves and Vibrations. Covers SHM, Doppler Effect, Beats, Stationary Waves, and Interference.
Wave: A disturbance transferring energy without transferring matter.
Mechanical Waves: Require medium (Sound, Water).
Electromagnetic Waves: No medium required (Light, Radio).
Transverse: Particles vibrate perpendicular to wave motion (Crests/Troughs).
Longitudinal: Particles vibrate parallel to wave motion (Compressions/Rarefactions).
Principle of Superposition: Resultant displacement is the algebraic sum of individual displacements.
Interference:
- Constructive: Path Diff = nλ (Max Amplitude).
- Destructive: Path Diff = (n + 0.5)λ (Min Amplitude).
Periodic variation in loudness due to interference of two waves of slightly different frequencies.
Beat Frequency: f_beat = f_1 - f_2. Used in tuning musical instruments.
Formed by superposition of two identical waves traveling in opposite directions. Contains Nodes (Zero disp) and Antinodes (Max disp).
Stretched String: f_n = n * f_1 (All harmonics).
Open Organ Pipe: Rich in harmonics (All present).
Closed Organ Pipe: Only odd harmonics present.
Apparent change in frequency due to relative motion between source and observer.
Source towards Observer: Frequency Increases (Wavelength decreases).
Source away from Observer: Frequency Decreases (Wavelength increases).
Applications: Radar, Sonar, Red Shift (Astronomy), Blood Flow measurement.