Unit: 4 Waves | BSc Physics Notes | Kannur University | Semester 3

 This unit explores the physics of wave motion, covering the nature, types, and mathematical description of mechanical waves. Topics include transverse and longitudinal waves, wave equation, superposition principle, interference, beats, and stationary waves. Understand how energy and information propagate through mediums using sinusoidal waveforms. Essential for Kannur University BSc Physics students, this unit also discusses wave velocity, phase difference, and boundary conditions in wave systems. Real-world applications like sound waves, musical instruments, and vibrating strings are explained with clarity. A must-study for conceptual clarity and strong fundamentals in classical physics.

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Semester 3 | Kannur University | Notes | BSc Physics

Unit 1:  Non inertial Systems and Fictious Forces: Link

Unit 2:  Central Force Motions: Link

Unit 3:  Harmonic Oscillator: Link

Unit 4:  Waves: Link

Here are illustrative diagrams depicting standing waves on a string and a general wave form, helpful for visualizing the concepts of nodes, antinodes, wavelength, amplitude, and wave propagation.

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Unit 4: Waves

BSc Physics (Kannur University – Semester 3)

1. Syllabus Overview

According to the Kannur University curriculum, this unit covers:

• Transverse vibrations of strings and wave propagation

• Longitudinal waves in gases and rods

• Standing waves in bounded media (strings, rods, and air columns)

• Modes of vibration

• Energy density and intensity of plane progressive waves
  (Kannur University)

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2. Core Concepts & Definitions

a) Wave Fundamentals

• What is a wave?
  A disturbance that transports energy (and momentum) through a medium (mechanical waves) or even through a vacuum (electromagnetic waves), without sending matter along.

• Key parameters:

  • Wavelength (λ): distance between successive crests or troughs

  • Amplitude (A): maximum displacement from equilibrium

  • Frequency (f) and Time period (T): inversely related by $T = 1/f$

  • Angular frequency (ω): $\omega = 2\pi f$

  • Wave speed (v): relates via $v = f \times \lambda$

b) Wave Equation & Wave Types

• General wave equation (1D):

  $$\frac{\partial^2 y}{\partial x^2} = \frac{1}{v^2} \frac{\partial^2 y}{\partial t^2}$$

• Solutions for progressive waves:

  $$y = f\bigl(t - \frac{x}{v}\bigr)\quad \text{or}\quad y = f\bigl(t + \frac{x}{v}\bigr)$$

• Harmonic (sine) wave:

  $$y = A \sin(kx - \omega t),\quad k = \frac{2\pi}{\lambda}$$

  (Studocu)

• Types of waves:

  • Transverse waves: oscillations perpendicular to direction of propagation

  • Longitudinal waves: oscillations parallel to direction of propagation (e.g., sound)

  • Plane waves vs spherical waves: planar front vs expanding spheres
    (sdmcollegehonnavar.com, adbcollege.org)

c) Standing Waves

• Arise from the superposition of two waves traveling in opposite directions.

• Key characteristics:

  • Nodes: points of zero displacement

  • Antinodes: points of maximum displacement

  • The diagrams at the top illustrate standing wave patterns on a string.

• Occur in:

  • Strings and rods (fixed endpoints)

  • Air columns (open/closed pipes)—modes depend on boundary conditions and can lead to resonances
    (Kannur University)

d) Energy in Waves

• Energy density and intensity in a plane progressive wave:

  • Energy is distributed between kinetic and potential forms

  • Energy intensity (power per unit area) depends on wave amplitude and frequency
    (Kannur University)

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3. Applications & Sample Examples

Phenomenon	Description
Vibrating String (e.g., guitar)	Formation of standing waves with harmonics; nodes and antinodes determine pitch.
Sound in Air Columns	Resonance in open or closed pipes; harmonic series depends on boundary conditions.
Energy Transport	Quantitative analysis of energy per unit length/area, intensity in waves like sound or strings.

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4. Sample Notes Outline

1. Introduction to Waves

   • Definitions and fundamental parameters

   • Mathematical representation (wave equation and its solution forms)

2. Types of Waves

   • Transverse vs longitudinal

   • Plane vs spherical

3. Wave Properties

   • Relationships between λ, f, v, ω, and k

4. Standing Waves & Resonance

   • Conditions for nodes and antinodes

   • Modes of vibration in different systems (strings, rods, air columns)

   • Resonant frequencies and harmonics

5. Energy Considerations

   • Energy density and current

   • Role of amplitude and frequency in intensity

6. Practical Applications & Examples

   • Musical instruments, acoustic resonance, energy transport

7. Practice Problems

   • Derive and solve the wave equation for given media

   • Analyze mode structure and frequencies in standing-wave systems

   • Calculate energy density and intensity for a given wave

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5. Study Tips

• Start with the basics: clearly understand wave definitions and key parameters.

• Use diagrams to visualize relations—identifying nodes/antinodes, wave profiles.

• Derive and practice wave equation transformations.

• Link formulas to physical scenarios: e.g., why amplitude affects intensity, how frequency and wavelength tie into speed.

• Solve problems that involve boundary conditions—especially resonance in strings and pipes.

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