Chapter 5: Waves

Overview

Waves are disturbances that propagate and transfer energy from one point to another without the transfer of matter. This chapter covers the fundamental properties of waves, including transverse and longitudinal waves, wave motion, damping and resonance, wave phenomena (reflection, refraction, diffraction, interference), and electromagnetic waves. Understanding wave behavior is crucial for applications in sound, light, communication, and many other areas of physics.

Learning Objectives

After completing this chapter, you will be able to:

• Differentiate between transverse and longitudinal waves
• Understand wave parameters (amplitude, wavelength, frequency, period)
• Apply wave equation calculations
• Explain damping and resonance phenomena
• Apply laws of reflection and refraction
• Understand diffraction and its conditions
• Analyze interference patterns and Young's double-slit experiment
• Describe the electromagnetic spectrum and its applications

Wave Fundamentals

Main Concept

A wave is a disturbance that propagates and transfers energy from one point to another without the transfer of matter.

Types of Waves

Transverse Waves

• Particles oscillate perpendicular to the direction of wave propagation
• Examples: Light waves, water waves, electromagnetic waves

Longitudinal Waves

• Particles oscillate parallel to the direction of wave propagation
• Consists of compressions and rarefactions
• Examples: Sound waves, seismic P-waves

Wave Types Comparison

Wave Propagation Visualization

Wave Parameters

Key Formulas

$$v = fλ$$ $$T = \frac{1}{f}$$

Where:

• v = Wave speed (m s⁻¹)
• f = Frequency (Hertz, Hz)
• λ = Wavelength (meters, m)
• T = Period (seconds, s)

Important Terms

• Amplitude (A): Maximum displacement from equilibrium position
• Wavelength (λ): Distance between two consecutive in-phase points
• Frequency (f): Number of complete oscillations per second
• Period (T): Time for one complete oscillation
• Wavefront: Line or surface connecting all points vibrating in phase

Wave Parameters Visualization

Wave Motion Diagram

Worked Example

Problem: A wave has a frequency of 500 Hz and wavelength of 0.8 m. Calculate: a) The wave speed b) The period of oscillation

Solution: a) Using v = fλ:

$$v = 500 \times 0.8 = 400 \text{ m s}^{-1}$$

b) Using T = 1/f:

$$T = \frac{1}{500} = 0.002 \text{ s} = 2 \text{ ms}$$

Answer: a) Wave speed = 400 m s⁻¹ b) Period = 2 ms

Damping and Resonance

Main Concept

Damping is the reduction in amplitude of an oscillating system due to energy loss. Resonance occurs when a system is forced to vibrate at its natural frequency by an external periodic force, causing maximum amplitude oscillations.

Key Principles

Damping

• Can be external (air resistance) or internal (strain and compression of particles)
• Causes gradual decrease in amplitude over time
• Affects both transverse and longitudinal oscillations

Resonance

• Occurs only when external force frequency equals natural frequency of system
• Can be useful (musical instruments) or dangerous (bridge collapses)
• Maximum amplitude occurs at resonance

Damping and Resonance Diagrams

Resonance Curve

Damping Effect Visualization

Important Terms

• Natural Frequency: Frequency at which a system vibrates when disturbed without external force
• Forced Oscillation: Oscillation produced by external periodic driving force

Did You Know?

The Tacoma Narrows Bridge collapse in 1940 was caused by resonance. The bridge's natural frequency matched the frequency of wind gusts, causing catastrophic oscillations that led to its collapse.

Wave Phenomena

Reflection of Waves

Main Concept

Reflection occurs when a wave strikes an obstacle and changes its direction of propagation.

Laws of Reflection

1. Angle of incidence (i) equals angle of reflection (r): $i = r$
2. Incident ray, reflected ray, and normal all lie in the same plane

Key Formulas

$$i = r$$

Important Terms

• Angle of Incidence (i): Angle between incident ray and normal
• Angle of Reflection (r): Angle between reflected ray and normal

Reflection Diagrams

Reflection Types

Refraction of Waves

Main Concept

Refraction is the change in direction of wave propagation when it passes from one medium to another with different densities.

Key Principles

• Refraction occurs due to change in wave speed
• When wave enters denser medium: speed decreases, wavelength decreases, bends towards normal
• Frequency remains constant during refraction

Key Formulas

$$v = fλ \text{ (f is constant, so v ∝ λ)}$$

Important Terms

• Deep Water: Less dense, high speed, large wavelength
• Shallow Water: More dense, low speed, small wavelength

Refraction Diagrams

Refraction Visualization

Diffraction of Waves

Main Concept

Diffraction is the spreading out of waves when they pass through a slit or around the edge of an obstacle.

Key Principles

• Diffraction effect is more pronounced when slit size or obstacle is smaller than or equal to wavelength (λ)
• After diffraction, wavelength, frequency, and speed remain unchanged
• Amplitude decreases because energy spreads over larger area

Important Conditions

For noticeable diffraction: $a ≤ λ$ (where $a$ = slit size)

Important Terms

• Slit: Narrow opening through which waves pass

Diffraction Diagrams

Diffraction Conditions

Single Slit Diffraction Pattern

Interference of Waves

Main Concept

Interference is the superposition (combination) of two or more waves from coherent sources.

Key Principles

Principle of Superposition: When two or more waves overlap, the resultant displacement at any point is the vector sum of individual displacements of each wave.

Types of Interference

Constructive Interference

• Occurs when crest meets crest or trough meets trough
• Resultant amplitude is maximum
• Path difference = nλ (where n = 0, 1, 2, ...)

Destructive Interference

• Occurs when crest meets trough
• Resultant amplitude is minimum or zero
• Path difference = (n + ½)λ (where n = 0, 1, 2, ...)

Young's Double-Slit Formula

$$λ = \frac{ax}{D}$$

Where:

• λ = Wavelength
• a = Distance between two coherent sources (slits)
• x = Distance between consecutive bright (or dark) fringes
• D = Perpendicular distance from source to screen

Important Terms

• Coherent Sources: Wave sources with same frequency and constant phase difference
• Antinode: Point where constructive interference occurs
• Node: Point where destructive interference occurs

Interference Diagrams

Young's Double-Slit Experiment

Interference Pattern Visualization

Electromagnetic Waves

Main Concept

Electromagnetic waves consist of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of energy propagation. They do not require a medium for propagation.

Key Principles

• All electromagnetic waves travel at the same speed in vacuum: speed of light ($c$)
• Electromagnetic spectrum is arranged by decreasing wavelength or increasing frequency:
  • Radio waves, Microwaves, Infrared, Visible light, Ultraviolet, X-rays, Gamma rays

Key Formulas

$$c = fλ$$

Where:

• c = Speed of light in vacuum = 3.0 × 10⁸ m s⁻¹

Important Terms

Electromagnetic Spectrum Properties

Electromagnetic Wave Structure

Electromagnetic Spectrum Visualization

EM Wave Generation and Detection

SPM Exam Tips

Common Mistakes to Avoid

1. Wave Type Confusion: Remember that particles in transverse waves oscillate perpendicular to wave direction
2. Units: Always use correct units (meters for wavelength, Hertz for frequency)
3. Frequency Constancy: Frequency remains constant during refraction and diffraction
4. Phase Difference: Understand the difference between coherent and incoherent sources

Problem-Solving Strategies

1. Identify Wave Type: Determine if transverse or longitudinal wave
2. List Parameters: Write down known quantities (λ, f, v, T)
3. Apply Appropriate Formula: Choose the right equation for the situation
4. Check Consistency: Verify that calculations make physical sense
5. Sketch Diagrams: Draw clear diagrams for reflection, refraction, and interference

Important Formula Summary

Practical Applications

Real-World Examples

1. Musical Instruments: Use resonance to produce specific frequencies
2. Noise Cancelling Headphones: Use destructive interference to cancel sound
3. Medical Ultrasound: Uses high-frequency sound waves for imaging
4. Radar Systems: Use electromagnetic waves for detection and ranging
5. Fiber Optics: Uses total internal reflection for data transmission

Safety Considerations

• Electromagnetic Radiation: Understand effects of different EM wave types
• Sound Pollution: Manage excessive sound frequencies
• Radiation Protection: Take precautions with high-frequency EM waves

Summary

This chapter covered essential wave concepts:

• Wave Types: Transverse and longitudinal waves with different properties
• Wave Parameters: Amplitude, wavelength, frequency, period, and their relationships
• Wave Phenomena: Reflection, refraction, diffraction, and interference
• Electromagnetic Waves: Spectrum, properties, and applications

Master these concepts to understand sound, light, and electromagnetic radiation - fundamental to modern technology and everyday life.

Practice Questions

1. A wave has a speed of 340 m s⁻¹ and frequency of 170 Hz. Calculate its wavelength.

2. Explain why sound waves cannot travel in vacuum but light can.

3. In Young's double-slit experiment, the distance between slits is 0.5 mm and the distance to the screen is 1.5 m. The distance between bright fringes is 1.5 mm. Calculate the wavelength of light used.

4. A ship's siren has a frequency of 200 Hz. Calculate the frequency heard by an observer when the ship moves towards the observer at 20 m s⁻¹. (Speed of sound = 340 m s⁻¹)

5. Describe how diffraction is used in various applications in everyday life.

---

• Chapter 4: Heat
• Chapter 1: Electronics (Form 5)