Simple Harmonic Motion

Simple Harmonic Motion (SHM) is the periodic motion characterized by oscillations about an equilibrium position, driven by a restoring force proportional to displacement.

Characteristics Of Oscillatory Motion

This section explores the key characteristics of oscillatory motion, focusing on the properties that define simple harmonic motion (SHM) and its relevance to waves.

Mass–spring System

The Mass-Spring System illustrates the principles of simple harmonic motion (SHM) through the interaction of mass and spring, focusing on restoring forces, energy conservation, and oscillation characteristics.

Simple Pendulum (Small-Angle Approximation)

The simple pendulum exhibits simple harmonic motion under small-angle approximations, allowing for a simplified equation of motion and energy analysis.

General Mathematical Form Of Shm

This section discusses the mathematical representations of Simple Harmonic Motion (SHM), specifically focusing on the cosine and sine forms of displacement, as well as how these relate to velocity and acceleration.

Energy In Shm: General Considerations

This section explores the energy transformations in simple harmonic motion (SHM), focusing on potential and kinetic energy.

Wave Model

Nature Of Waves

This section defines waves, explores their classifications, and discusses key parameters that describe them.

Wave Parameters

This section addresses the fundamental parameters of waves, including amplitude, wavelength, frequency, and wave speed.

Transverse Versus Longitudinal Waves

This section explains the differences between transverse and longitudinal waves, highlighting their characteristics and mathematical descriptions.

Derivation Of The One-Dimensional Wave Equation

This section describes the derivation of the one-dimensional wave equation for a uniform string under tension.

Wave Phenomena

Wave phenomena encompass reflection, refraction, diffraction, and interference, which occur when waves interact with boundaries or media.

Reflection

Reflection describes how waves behave when they encounter a boundary, highlighting the law of reflection and phase changes upon reflection.

Refraction

Refraction is the bending of waves as they pass from one medium to another, affecting speed and direction.

Diffraction

Diffraction refers to the spreading and bending of waves when encountering obstacles or apertures comparable to their wavelength.

Interference

Interference is the phenomenon that occurs when two or more waves overlap, leading to a resultant wave that can be either amplified or diminished.

Applications Of Wave Behaviour

This section discusses practical applications of wave behavior, including diffraction gratings, interferometry, and acoustic applications.

Standing Waves And Resonance

This section focuses on the formation of standing waves through the superposition of two waves traveling in opposite directions and introduces the concept of resonance in oscillatory systems.

Formation Of Standing Waves

Standing waves are formed when two identical waves traveling in opposite directions interfere with each other, resulting in nodes and antinodes.

Standing Waves On A String Fixed At Both Ends

Standing waves form when two identical waves travel in opposite directions along a medium, resulting in fixed points called nodes and points of maximum amplitude called antinodes.

Standing Waves In Air Columns

Standing waves occur in air columns when two waves of equal and opposite direction superpose, creating a pattern of nodes and antinodes, depending on whether the ends are open or closed.

Resonance

Resonance occurs when a system is driven at a frequency close to its natural frequency, leading to increased amplitude of oscillation.

Doppler Effect (Hl Only)

The Doppler Effect describes the change in observed frequency of a wave due to the relative motion between the source and observer.

Phenomenon Of Frequency Change

The Doppler effect describes how the observed frequency of a wave changes due to the relative motion between the source and the observer.

Application In Astronomy

This section explores the Doppler effect in astronomy, focusing on redshift and blueshift, which provide critical insight into the motion of celestial objects.

Application In Medical Imaging

This section discusses the applications of the Doppler Effect in medical imaging, primarily through techniques like Doppler ultrasound and echocardiography.