Lesson Overview

Unit 3 explores oscillatory systems, wave behaviour, sound, and electromagnetic waves. It includes SHM, wave types, wave properties, interference, beats, stationary waves, resonance, Doppler effect, and EM waves including LASER. This unit provides the conceptual foundation for understanding vibrations, sound production, and the nature of light.

1. Core Concepts (Short Notes)

3.1 Simple Harmonic Motion (SHM)

• SHM: Motion where acceleration is proportional to displacement and opposite in direction.

• Equation: a = –ω²x

• Period (T): Time for one cycle.

• Frequency (f): Number of cycles per second.

• Phase and phase difference.

3.2 Wave Motion

• Mechanical waves: Require a medium.

• Types: Longitudinal & Transverse.

• Wave parameters: Wavelength (λ), Frequency (f), Speed (v), Amplitude (A).

• Equation: v = fλ

3.3 Wave Properties

• Reflection

• Refraction

• Diffraction

• Interference

• Superposition principle

• Beats

3.4 Stationary Waves & Vibrations

• Formed by superposition of two opposite-travelling waves.

• Nodes (N) & antinodes (A).

• Strings and air columns.

• Harmonics & overtones.

3.5 Sound Waves

• Longitudinal waves.

• Speed depends on temperature, pressure, humidity.

• Resonance in tubes.

3.6 Doppler Effect

• Apparent change in frequency due to motion of source or observer.

3.7 Electromagnetic Waves (EM Waves)

• Do not require a medium.

• Produced by oscillating electric & magnetic fields.

• Wide spectrum: Radio → Gamma.

• LASER: Light Amplification via Stimulated Emission.

2. Detailed Notes for Each Section

3.1 Simple Harmonic Motion (SHM)

Characteristics of SHM

• Restoring force ∝ displacement.

• Acceleration: a = –ω²x.

• Displacement: x = A sin(ωt + φ).

• Velocity: v = ω√(A² – x²).

• Energy in SHM:

  • PE = ½ kx²

  • KE = ½ k(A² – x²)

Examples of SHM

• Simple pendulum (small angles)

• Mass–spring system

• Vibrating strings

3.2 Wave Motion

Definitions

• Wavelength (λ): Distance between identical points.

• Frequency (f): Waves per second.

• Amplitude (A): Maximum displacement.

• Speed (v): fλ.

Types of Mechanical Waves

• Transverse: Particles vibrate perpendicular to direction of wave.

• Longitudinal: Particles vibrate parallel.

Graphical Representation

• Displacement–distance graphs.

• Displacement–time graphs.

3.3 Wave Properties

1. Reflection

• Angle of incidence = angle of reflection.

• Rigid boundary: Phase change of π.

• Soft boundary: No phase change.

2. Refraction

• Bending due to change in wave speed.

• Water → air: bends away from normal.

3. Diffraction

• Spreading of waves when passing through slit.

• Increases when slit size ≈ wavelength.

4. Interference

• Constructive: Waves in phase → large amplitude.

• Destructive: Waves out of phase → cancellation.

5. Beats

• Produced when two close frequencies interfere.

• Beat frequency = |f₁ – f₂|.

3.4 Stationary Waves & Resonance

Formation

• Occurs when similar waves travel in opposite directions.

• Nodes: zero amplitude.

• Antinodes: maximum amplitude.

Strings

• First harmonic: f₁ = v/2L.

• Second harmonic: 2f₁.

• Third harmonic: 3f₁.

Air Columns

• Open–open: f₁ = v/2L.

• Open–closed: f₁ = v/4L.

• Higher harmonics follow odd multiples for open–closed.

3.5 Sound Waves

Speed of Sound in Air

• v = √(γRT/M)

• Increases with:

  • Temperature

  • Humidity

  • Lower molecular mass

Resonance in Tubes

• End correction required.

• Closed tube: Only odd harmonics.

Sound Intensity & Levels

• Intensity ∝ amplitude².

• Measured in decibels (dB).

3.6 Doppler Effect

Observations

• Frequency increases when source approaches observer.

• Decreases when moving away.

Equations

When observer moves:

When source moves:

3.7 Electromagnetic Waves

Characteristics

• Travel at 3×10⁸ m/s.

• Transverse waves.

• Electric and magnetic fields oscillate at right angles.

EM Spectrum (Low → High Frequency)

1. Radio

2. Microwave

3. Infrared

4. Visible

5. Ultraviolet

6. X-rays

7. Gamma rays

LASER

• Monochromatic

• Coherent

• Directional

• Based on stimulated emission of radiation.

3. Formula Summary for Unit 3

• a = –ω²x

• x = A sin(ωt)

• v = fλ

• Beat frequency = |f₁ – f₂|

• f₁ (string) = v/2L

• f₁ (closed tube) = v/4L

• Doppler equations as above

• Speed of sound: v = √(γRT/M)

4. Common Mistakes to Avoid

• Confusing transverse and longitudinal waves.

• Forgetting that sound requires a medium.

• Misidentifying nodes/antinodes.

• Using wrong slit width for diffraction questions.

• Incorrect substitution in Doppler formula.

5. Exam Tips

• Draw clear wave diagrams.

• Label λ, A, f clearly.

• For interference, always state phase difference.

• Use beat frequency to identify tuning mismatches.

• For EM waves, remember: higher frequency → higher energy.

6. Quick Revision Table