Physics Chapter 12: Mechanical Waves

Chapter 12 Lecture Topics

• The lecture covers mechanical waves, periodic mechanical waves, wave speeds, and the mathematical description of a wave.
• Additional topics include reflections, superposition, standing waves, normal modes, longitudinal standing waves, interference, sound, hearing, sound intensity, beats, and the Doppler effect.
• The goals of the chapter include describing mechanical waves, understanding superposition, standing waves, and sound, presenting sound as a standing longitudinal wave, demonstrating wave interference, studying sound intensity and beats, solving for frequency shifts (Doppler effect), and examining applications of acoustics and musical tones.
• Mechanical waves involve the motion of a substance (medium) through which they move.
• A wave is an organized disturbance that travels with a defined wave speed.
• Waves transfer energy, but not matter.
• Electromagnetic waves (EM waves) include visible light, radio waves, microwaves, and x-rays; they don’t require a medium to travel.
• Matter waves describe the wave-like characteristics of material particles at an atomic scale.

Types of Mechanical Waves

• Transverse waves: particle motion is perpendicular to wave motion (e.g., a wave on a string).
• Longitudinal waves: particle motion is parallel to wave motion (e.g., sound waves).
• Water waves are a complex mix of both transverse and longitudinal motions.
• Earthquake waves are important examples of both transverse (S waves) and longitudinal (P waves).

Wave Speed

• Wave speed depends on the properties of the medium, not the properties of the wave.
• For strings, wave speed is determined by tension and linear density (mass per unit length).
• Higher tension typically means higher wave speed; higher linear density means lower wave speed.
• Sound wave speed in a gas is affected by temperature and molecular mass.
• Warmer temperature and lower molecular mass typically increase wave speed.
• Wave speed in liquids and solids is generally faster than in gases.
• The speed of electromagnetic waves (e.g., light) in a vacuum is a constant (approximately 3.00 × 10⁸ m/s).

Mathematical and Graphical Descriptions

• A snapshot graph shows displacement as a function of position at a single time.
• A history graph shows displacement as a function of time at a single position.
• Sinusoidal waves have a repeating pattern; their displacement can be described mathematically.
• Important relationships include:
• v = λf
• the speed of the wave equals the wavelength multiplied by the frequency.

Other Concepts

• Wave reflections can occur at boundaries, causing inversions or no inversions depending on the boundary conditions.
• Wave superposition describes how waves interact when they overlap; this can result in constructive interference, destructive interference, or a complex pattern.
• Standing waves occur when waves interfere to create a pattern of nodes (no motion) and antinodes (maximum motion).
• Different resonant patterns may occur when the length of the medium or cavity is restricted in various ways

Additional Examples

• Worked examples are available in the text (pages).
• Examples include how long it takes for a spider to detect an insect landing on its web, calculating the speed of a wave on a string, determining the fundamental frequencies for various sounds, determining the velocity of sound, and sound intensity (decibel levels).

This quiz explores the fundamental concepts of mechanical waves, including their properties, behavior, and applications. Topics such as wave speed, reflection, interference, sound intensity, and the Doppler effect are covered. Test your understanding of how waves transfer energy and their mathematical descriptions.