Waves, Sound, and Electricity

Overview

This study guide reviews key concepts from Physics 103, focusing on the topics of waves, sound, and electricity. These topics are essential for understanding physical phenomena in both classical and modern physics, and are directly relevant to chapters 11, 12, and 16–17 of a typical college physics curriculum.

Wave Motion

Basic Properties of Waves

Waves are disturbances that transfer energy through a medium or space. The medium's particles oscillate but do not travel with the wave.

• Waveform: A graphical representation of a wave at a given instant. High points are crests, low points are troughs.

• Wavelength (): The distance between successive crests or troughs.

• Frequency (): Number of wave cycles passing a point per unit time.

• Period (): Time for one complete cycle; .

• Wave velocity (): Speed at which the wave propagates; .

Example: Water waves on a lake show crests and troughs moving outward, while water molecules oscillate up and down.

Mathematical Representation of a Traveling Wave

The displacement of a point on a wave as a function of position and time is:

• Where is amplitude, is the wave number, and is angular frequency.

Types of Waves

• Transverse Waves: Particle motion is perpendicular to wave direction (e.g., waves on a string).

• Longitudinal Waves: Particle motion is parallel to wave direction (e.g., sound waves).

Standing Waves and Resonance

Standing Waves on a String

Standing waves form when two waves of the same frequency travel in opposite directions and interfere. Nodes are points of zero amplitude; antinodes are points of maximum amplitude.

• Fundamental frequency: Lowest frequency standing wave.

• Harmonics: Higher frequency standing waves, integer multiples of the fundamental.

• Wavelengths for string fixed at both ends: ,

• Frequencies:

Speed of a Wave on a String

• Where is tension, is linear mass density ()

Sound Waves

Nature of Sound

Sound waves are longitudinal waves that travel through a medium by compressions and rarefactions.

• Speed of sound in air: (where is temperature in °C)

• Speed in liquids: (Bulk modulus , density )

• Speed in solids: (Young's modulus , density )

Categories of Sound Waves

• Audible: 20 Hz to 20,000 Hz

• Infrasonic: Below 20 Hz

• Ultrasonic: Above 20,000 Hz

Standing Waves in Air Columns

• Open at both ends: , ,

• Closed at one end: , ,

Intensity and Decibels

• Intensity (): Power per unit area,

• Decibel level (): , W/m2

Doppler Effect

The observed frequency changes due to relative motion between source and observer.

• General formula:

• = speed of sound, = observer speed (positive toward source), = source speed (positive away from observer)

Shock Waves and Sonic Boom

• Occurs when source moves faster than wave speed in medium.

• Produces a cone-shaped shock wave; angle given by

Electricity: Charge and Electric Field

Electric Charge

• Fundamental property: Two types: positive and negative.

• Conservation: Total charge in an isolated system is constant.

• Quantization: , C

Conductors and Insulators

• Conductors: Allow free movement of charge (e.g., metals).

• Insulators: Do not allow free movement of charge (e.g., glass, rubber).

Coulomb’s Law

• Force between two point charges:

• Nm2/C2

• Force is attractive for opposite charges, repulsive for like charges.

Electric Field

• Definition:

• Field due to point charge:

• Direction: Away from positive, toward negative charge.

Electric Field Lines

• Lines start on positive charges, end on negative charges.

• Density of lines indicates field strength.

• Field is tangent to lines at every point.

Motion of Charged Particles in Electric Fields

• Charged particle experiences force .

• Acceleration:

• Direction depends on sign of charge.

Electric Potential and Potential Energy

• Potential energy change: (for uniform field)

• Potential difference:

• Work:

• Unit: Volt (V),

Key Equations Table

Summary

• Waves transfer energy without transferring matter; sound is a longitudinal wave requiring a medium.

• Standing waves and resonance are key in musical instruments and physics experiments.

• Sound intensity is measured in decibels; the Doppler effect explains frequency shifts due to motion.

• Electric charge is quantized and conserved; Coulomb’s law describes the force between charges.

• Electric fields and potentials are fundamental to understanding electrical interactions.