19_LectureOutline

Chapter 19: Vibrations and Waves

Introduction

• This chapter covers fundamental concepts of vibrations and waves, including:

  • Vibrations of a Pendulum

  • Wave Description

  • Wave Speed

  • Transverse Waves

  • Longitudinal Waves

  • Wave Interference

  • Standing Waves

  • Doppler Effect

  • Bow Waves

  • Shock Waves

Good Vibrations

• A vibration is a periodic wiggle in time.

• A wave is a periodic wiggle in both space and time, extending from one place to another.

  • Examples of waves:

    • Electromagnetic Waves: Light (needs no medium)

    • Mechanical Waves: Sound (requires a medium)

Definitions of Waves and Vibrations

• Vibration: Wiggle in time

• Wave: Wiggle in space and time

Vibrations of a Pendulum

• A simple pendulum consists of a stone suspended at the end of a string.

• The pendulum's swing rate:

  • Depends only on the length of the pendulum.

  • Mass does not affect the swing rate (similar to mass not affecting ball fall rate).

• Period: The duration of one complete to-and-fro swing.

  • Longer pendulum length = longer period (similar to free-fall duration).

Understanding Period through Examples

• If a 1-meter-long pendulum (1 kg) changes its bob to a mass of 2 kg, the period:

  • Remains the same; period depends on the length, not mass.

• If the bob lengthens to 2 meters, the period:

  • Increases with increasing length.

Wave Description

• Waves can be visually represented using a sine curve:

  • This is created by tracing the path of a swinging pendulum with sand that drops onto paper.

  • A marking pen also illustrates sine curves with vertical movement traced over horizontal time.

Wave Characteristics

• Crests: High points of the wave.

• Troughs: Low points of the wave.

• Amplitude: Distance from the midpoint to the crest or trough.

• Wavelength: Distance between successive crests or troughs.

Frequency and Period

• Frequency: How frequently a vibration occurs, measured in Hertz (Hz).

  • 1 Hz = 1 vibration/second.

  • Mechanical vibrations: a few Hz.

  • Sound frequencies: a few hundred to thousand Hz.

  • Radio waves: up to millions Hz (MHz).

  • Cell phones: billions Hz (GHz).

• Period (T): Time to complete one vibration, inversely related to frequency.

  • Example: 2 Hz frequency corresponds to a 0.5 second period.

Wave Motion

• Wave Motion: Waves transport energy without transporting matter.

  • When a stone is dropped in water, ripples travel without moving water across the pond.

• Wave Speed: Distance traveled by waves, determined by frequency and wavelength.

  • Example: Wave speed formula: speed = frequency × wavelength.

Types of Waves

• Transverse Waves: Medium vibrates perpendicularly to the direction of energy transfer (side-to-side).

  • Examples: Vibrations of musical instrument strings, light waves, transverse seismic waves (S-waves).

• Longitudinal Waves: Medium vibrates parallel to the energy transfer direction (back-and-forth).

  • Composed of compressions and rarefactions.

  • Examples: Sound waves, longitudinal seismic waves (P-waves).

Wave Interference

• Wave Interference: The interaction of waves when they meet, can cause:

  • Constructive Interference: Amplitudes add, creating a wave of increased amplitude.

  • Destructive Interference: Crest of one wave overlaps the trough of another, reducing overall amplitude.

Standing Waves

• Standing Waves: Created when waves are reflected back, forming a pattern with stationary nodes (minimal displacement) and antinodes (maximal displacement).

  • Examples: Waves in strings, sound waves in instruments.

Doppler Effect

• Describes frequency changes in waves due to motion:

  • Sound Waves: A pitch increase as the source approaches, decrease as it moves away.

  • Light Waves: Blue shift (increase) as a light source approaches; red shift (decrease) as it recedes.

Bow Waves and Shock Waves

• Bow Waves: Occur when waves superimpose to create a barrier when objects travel faster than the wave speed.

• Shock Waves: Formed by objects traveling faster than sound, resulting in overlapping spherical patterns that create a cone. This generates sonic booms from supersonic aircraft.