6.01 -- Intro to Travelling Waves

Introduction to Travelling Waves

• The goal of this lesson is to introduce key concepts in wave theory that include:

  • Differences between mechanical and electromagnetic (EM) waves

  • Differences between transverse and longitudinal waves

  • Proper naming of parts of waves.

• This content corresponds to specific sections in the study guide (Kirk 2014) and textbooks (Tsokos, 6th ed), across various topics related to wave models and phenomena, totaling significant hours for both Standard Level (SL) and Higher Level (HL) students.

Key Concepts Related to Wave Understanding

• Expected Understandings:

  • Understand the nature and differences between transverse and longitudinal waves.

  • Utilize concepts related to wavelength, frequency, period, and wave speed linked to the wave equation.

  • Comprehend various properties of sound waves and electromagnetic waves.

  • Explore how waves travel in two and three dimensions, described via wave fronts and rays.

  • Analyze superposition of waves and wave pulses, including conditions for constructive interference.

• Standing Waves:

  • Explore the formation of standing waves via the superposition of two identical waves moving in opposite directions, including the concepts of nodes and antinodes.

  • Assess the relative amplitude and phase differences along a standing wave.

  • Understand factors contributing to resonance, including natural frequency and amplitude, and the impact of damping on oscillation.

Basics of Oscillation

• Oscillation:

  • Defined as repetitive, periodic motion about a fixed point (equilibrium), characterized by a predictable pattern. Each cycle of motion takes a certain time known as the period.

• Simple Harmonic Motion (SHM):

  • A specific type of oscillation characterized by a restoring force that opposes and is proportional to displacement.

  • Mathematical modeling of SHM will involve periodic or sinusoidal functions, highlighting links between different wave behaviours.

Wave Properties

• A wave is fundamentally a disturbance that transfers energy without causing net displacement of particles over time. In contrast to SHM, which does not transfer energy, waves propagate energy across distances.

• Travelling Wave:

  • Defined as a continuous wave where movement in the direction of propagation is detectable, characterized by active energy transmission.

• A wave pulse represents the movement of a single oscillation and serves as a fundamental example to observe wave behaviours.

• A continuous wave involves a series of regular oscillations contrasting with isolated wave pulses.

Mediums & Types of Waves

• Medium:

  • The physical substance through which a wave travels; waves cannot propagate through a vacuum as there is no medium.

  • Wave propagation occurs due to the displacement of particles within the medium transmitting kinetic energy and momentum.

Classification of Waves

• Mechanical Waves:

  • Require a physical medium (e.g., water, air) for propagation, originating from movement and transmitting mechanical energy.

  • Examples include sound waves and waves on strings.

• Electromagnetic Waves:

  • Can travel through a vacuum, characterized by electric and magnetic components that are perpendicular to each other.

  • These waves include light and other forms of radiation.

Wave Types and Their Characteristics

• Transverse Waves:

  • Displacement of particles is perpendicular to the wave direction.

• Longitudinal Waves:

  • Also known as compression waves where the displacement of particles is parallel to the direction of energy propagation.

• Surface Waves:

  • A combination of transverse and longitudinal waves, resulting in particle motion that follows a circular or ovoid path.

Wavefronts and Rays

• Wavefront:

  • Defined as a surface representing peaks of displacements normal to the direction of wave propagation, illustrated through a series of parallel lines.

• Ray:

  • A line normal to wavefronts indicating the direction of propagation, commonly used to discuss EM waves and wave reflection.