Physics 20 Unit 7: Waves Notes and Practice

Physics 20 Unit 7: Waves Notes and Practice

Outcomes Assessed

• D2: Describe, analyze, and explain the properties and behavior of mechanical waves.

• D3: Describe, analyze, and explain wave phenomena.

Lessons Overview

• Lesson 1: Waves in One Dimension

• Lesson 2: Waves in Two Dimensions

• Lesson 3: Resonance and Sounds

• Lesson 4: The Doppler Effect

Lesson 1: One-Dimensional Waves

Mechanical Waves

• There are two basic ways to transmit or move energy from one place to another:

  • Kinetic Energy: Moving an object from one location to another via kinetic energy.

  • Waves: Moving energy in the form of waves.

Definition of Waves

• Waves move energy through distances as a result of vibratory motions.

• Two general classes of waves:

  • Electromagnetic Waves: Can move through objects or through the vacuum of space. (studied in Physics 30)

  • Mechanical Waves: Require a medium through which they can travel; cannot travel through a vacuum.

Types of Mechanical Waves

• Transverse Waves:

  • Particles in the medium vibrate perpendicular to the direction of wave energy.

  • Features include crests (positive amplitude) and troughs (negative amplitude).

• Longitudinal Waves:

  • Particles in the medium vibrate parallel to the direction of wave energy.

  • Wave advances by causing compressions and rarefactions within the medium.

  • Compression: Region of higher particle concentration.

  • Rarefaction: Region where particles are further apart.

  • Upon passage of the wave, no trace of it remains.

Wave Pulses vs. Waves

• Wave Pulse: A disturbance with a beginning and an end.

• Wave Train: A continuous series of pulses.

Wave Properties

Wavelength, Amplitude, Period, and Frequency

• Amplitude: Maximum displacement of the medium from the equilibrium position.

• Wavelength, $ext{λ}$: Distance between two points in the exact same phase on the wave.

• Period, $T$: Time to travel one wavelength.

• Frequency, $f$: Number of wavelengths occurring in one second.

Relationship between Frequency and Period

• $f = rac{1}{T}$

• Note: Wavelength, period, and frequency do not depend on amplitude.

  • Amplitude Related to Energy: Greater amplitude indicates higher energy.

  • Frequency Related to Vibratory Rate: Higher vibratory rate corresponds to higher frequency.

Speed and the Universal Wave Equation

• The speed of various waves differs based on the medium.

  • Example: Sound travels faster in rocks than in air due to higher density.

  • Rigidity: Higher rigidity results in higher sound speed.

Universal Wave Equation

• Relates wave speed, frequency, and wavelength:

• $v = f imes ext{λ}$

• Example Problems:

  • A series of waves with $ext{λ} = 2.5 ext{ m}$ and $f = 50 ext{ Hz}$ yields a speed:

  • $v = 50 ext{ Hz} imes 2.5 ext{ m} = 125 ext{ m/s}$

  • A wave series with $ext{λ} = 10 ext{ m}$ and speed of $300 ext{ m/s}$ yields frequency:

  • $f = rac{v}{ ext{λ}} = rac{300 ext{ m/s}}{10 ext{ m}} = 30 ext{ Hz}$

Reflection and Transmission of Waves

• When a wave or pulse meets a boundary, some energy is reflected.

• Reflection behavior is contingent on boundary nature (fixed vs. free):

  • Fixed End: Reflected pulse is inverted.

  • Free End: Reflected pulse remains upright.

Partial Reflection

• When transitioning between different mediums, wave energy experiences partial reflection and transmission.

  • Slow to Fast Medium: Reflected wave is upright.

  • Fast to Slow Medium: Reflected wave is inverted.

  • Amplitude of the incident pulse divides into reflected and transmitted waves.

Interference

Superposition Principle

• When two waves encountering one another, they pass through each other rather than reflect.

  • The resulting amplitude is the sum of their individual amplitudes.

  • Constructive Interference: When crests meet crests and troughs meet troughs, resulting in a larger waveform.

  • Destructive Interference: When crests meet troughs and troughs meet crests, canceling amplitude effects.

Lesson 1 Practice Exercises

• Tasks: Measure wavelengths, determine crests and troughs, compute frequency and speed, sketch waves, and match terminologies with definitions.

Lesson 2: Waves in Two Dimensions

Overview

• Two-dimensional waves (such as water ripples) share key properties with one-dimensional waves but exhibit unique manifestations.

Wavefront and Wave Ray Diagrams

• Two kinds of diagrams represent these waves:

  • Wavefront Diagrams: Lines represent crests, arrows indicate motion direction.

  • Wave Ray Diagrams: Equivalent representation of wavefronts moving directionally.

Reflection

• A wave striking a solid boundary undergoes reflection (similar to a basketball bounce).

• Law of Reflection:

  • $heta<em>i = heta</em>r$; angles measured from an imaginary normal line perpendicular to the surface.

Refraction

• Waves maintain constant frequency in a medium; entering a different medium causes changes in speed and wavelength, while frequency remains constant.

• Forward and backward bending of waves occurs based on speed change (towards or away from the normal).

Diffraction

• Refers to the bending and spreading of waves around obstacles or through openings.

• Huygen's Principle: Each point on a wavefront acts as a source for new spherical waves.

• Observations reveal wave reformation around obstacles.

Interference Patterns

• In two dimensions, interference results in a pattern of antinodes (constructive interference) and nodes (destructive interference) depending on wave source distance and characteristics.

Practice Exercises

• Exercises include laws of reflection/refraction, drawing resulting diagrams, calculating angles of reflection, and detailing sound wave behavior with respect to distance and interference.

Lesson 3: Resonance and Sounds

Mechanical Resonance

• Objects possess a natural frequency, the frequency at which they naturally vibrate.

• Forced Frequency: When an external force maintains oscillation at the resonant frequency.

• Mechanical Resonance: Increased amplitude occurs when the forced frequency matches the natural frequency.

  • Can lead to destructive outcomes (e.g., breaking glass via matched vibrational frequencies).

  • E.g., soldiers marching can collapse bridges when their vibrations match the resonance frequency.

Standing Waves

• When two waves of identical amplitude interfere, they create a standing wave.

  • Contains nodes (minimum amplitude) and antinodes (maximum amplitude), with neighboring nodes/antinodes spaced by $rac{1}{2} ext{λ}$.

Resonance in Air Columns

• Nodes at closed ends; antinodes at open ends.

• Changes in air column length adjust frequencies within the pipe (e.g., blowing into bottles).

Practice Exercises

• Tasks include calculating frequencies and resonant lengths using provided examples.

Lesson 4: The Doppler Effect

Definition and Impact

• Doppler Effect: Change in frequency perceived due to the motion of source/observer.

  • E.g., approaching sources increase perceived pitch; receding sources decrease it.

Formulas for the Doppler Effect

• For moving source (with stationary observer and moving toward observer), the frequency heard can increase or decrease depending on the relative motion.

• Example Calculations: Include sound and light frequencies with distances services (e.g., moving trains, astronomical observations).

• Situational examples yield specific frequency adjustments based on source motion.

Practice Exercises

• Exercises involve calculating frequency adjustments in various scenarios, providing experience with the Doppler Effect in real-world contexts.