#AP Physics 2: Waves - The Ultimate Study Guide 🌊

Hey there, future physics pro! 👋 This guide is your one-stop shop for mastering waves in AP Physics 2. Let's make sure you're feeling confident and ready to ace that exam!

#What is a Wave?

At its core, a wave is a disturbance that transfers energy through a medium (a substance or material). Think of it like a ripple in a pond or a stadium wave – energy moves, but the water or people don't travel with it. 💡

• Energy is transferred without transferring matter.
• Particles in the medium return to their original position.

#Types of Waves

Waves come in different flavors, each with unique characteristics. Here's a breakdown:

• Transverse Wave: Particles move perpendicular to the wave's direction. Think of a rope being shaken up and down.
• Longitudinal Wave: Particles move parallel to the wave's direction. Think of a slinky being pushed and pulled.
• Mechanical Wave: Requires a medium to travel. These can be either longitudinal or transverse.
• Electromagnetic Wave: Doesn't need a medium; can travel through a vacuum. Always transverse.

Pay close attention to the differences between transverse and longitudinal waves, and mechanical and electromagnetic waves. These concepts are fundamental and frequently tested.

#Longitudinal vs. Transverse Waves

• Longitudinal Waves:
  • Disturbance travels parallel to the wave direction.
  • Involves compressions (particles close) and rarefactions (particles far apart).
  • Example: Sound waves
• Transverse Waves:
  • Disturbance travels perpendicular to the wave direction.
  • Involves crests (high points) and troughs (low points).
  • Example: Water waves

#Mechanical vs. Electromagnetic Waves

• Mechanical Waves:
  • Require a medium (like air, water, or a solid) to travel.
  • Transfer energy through particle movement.
  • Examples: Sound waves, surface waves
• Electromagnetic Waves:
  • Do not require a medium; can travel through a vacuum.
  • Transfer energy through oscillating electric and magnetic fields.
  • Examples: Light, radio waves, X-rays

#Anatomy of Waves

Let's break down the key parts of a wave: 🔎

#Transverse Waves:

Image source: Wikimedia Commons

#Longitudinal Waves:

Image source: Wikimedia Commons

• Wavelength (λ): The length of one complete wave cycle (crest to crest or trough to trough).
• Amplitude (a): The height of the wave from rest to maximum displacement. Amplitude is proportional to the energy of the wave.
• Crest: The highest point of a transverse wave.
• Trough: The lowest point of a transverse wave.
• Compression: Region of maximum density in a longitudinal wave.
• Rarefaction: Region of minimum density in a longitudinal wave.
• Frequency (f): The number of waves per second, measured in Hertz (Hz).
• Period (T): The time for one complete wave cycle, measured in seconds (s).
• Polarization: The direction of a wave's vibration. Only transverse waves can be polarized.

#Wave Equations

Here are the key equations you'll need:

• Period and Frequency: $$T = \frac{1}{f}$$ $$f = \frac{1}{T}$$

• Wave Speed: $$v = \frac{distance}{time}$$ $$v = \frac{\lambda}{T}$$ $$v = \lambda f$$

#Example Problem: Polarization Analysis

Let's tackle a problem that combines multiple concepts:

Problem: You have a graph of a mechanical wave's displacement over time and distance. The wave travels in the positive x direction.

1. Is the wave polarized?
2. If so, what is the polarization direction?
3. Why must the vibration be perpendicular to the energy propagation?

Solution:

1. Polarized: The waveform is asymmetrical and has a specific orientation.
2. Vertical Polarization: The waveform is oriented along the y-axis.
3. Perpendicular Vibration: In a polarized wave, the vibration is perpendicular to the direction of energy propagation. The energy moves in the x-direction, while the particles vibrate in the y-direction.

#Final Exam Focus

• High-Priority Topics:
  • Distinguish between transverse and longitudinal waves.
  • Understand mechanical vs. electromagnetic waves.
  • Relate wavelength, frequency, and speed using equations.
  • Analyze wave graphs to determine properties.
  • Understand the concept of polarization
• Common Question Types:
  • Multiple Choice: Conceptual questions on wave properties, types, and behavior.
  • Free Response: Graph analysis, calculations involving wave speed, frequency, and wavelength; explanations of polarization
• Last-Minute Tips:
  • Time Management: Quickly identify what each question is asking. Don't spend too much time on one problem.
  • Common Pitfalls: Watch for tricky wording, especially when dealing with wave speed and medium changes. Remember that wave speed depends on the medium.
  • Strategies: Draw diagrams to visualize waves, label axes on graphs carefully, and use units to guide your calculations.

#Practice Problems

Practice Question

1. Which of the following statements about the speed of waves on a string are true? I. The speed depends on the tension in the string II. The speed depends on the frequency III. The speed depends on the mass per unit length of the string.

   A) II only B) I and II only C) I and III only D) II and III only E) I, II and III

2. A wave has a frequency of 50 Hz. The period of the wave is:

   A) 0.010 s B) 0.20 s C) 7 s D) 20 s E) 0.020 s

3. If the frequency of sound is doubled, the wavelength:

   A) halves and the speed remains unchanged B) doubles and the speed remains unchanged C) is unchanged and the speed doubles D) is unchanged and the speed halves E) halves and the speed halves

4. An observer hears a sound with a frequency of 400 Hz. Its wavelength is approximately:

   A) 0.85 m B) 1.2 m C) 2.75 m D) 13.6 m E) 44 m

5. As sound travels from steel into air, both its speed and its:

   A) wavelength increase B) wavelength decrease C) frequency increase D) frequency decrease E) frequency remain unchanged

Answers:

1. C: Based on the formula
2. E: Use T = 1/f
3. A: Frequency and wavelength are inverse
4. A: Speed of sound is 340, use v = f λ
5. B: When sound travels into less dense medium, its speed decreases (unlike light) … however, likeall waves when traveling between two mediums, the frequency remains constant. Based onv = f λ, if the speed decreases and the frequency is constant then the λ must decrease also.

Free Response Question:

Context: A transverse wave is traveling along a string. The figure below shows the displacement of the string as a function of position at a given time. The wave is traveling to the right with a speed of 2.0 m/s.

(a) Determine the wavelength of the wave. (b) Determine the frequency of the wave. (c) Determine the period of the wave. (d) Draw a graph of the displacement of the string as a function of time at the position x = 0. Label the axes with appropriate units. (e) If the tension in the string is increased, how does this affect the wave speed and the wavelength? Explain your reasoning.

Scoring Breakdown:

(a) Wavelength (2 points)

• 1 point for correctly identifying the wavelength from the graph (e.g., 2.0 m)
• 1 point for including units

(b) Frequency (2 points)

• 1 point for using the correct formula (v = fλ or f = v/λ)
• 1 point for the correct answer with units (e.g., 1.0 Hz)

(c) Period (2 points)

• 1 point for using the correct formula (T = 1/f)
• 1 point for the correct answer with units (e.g., 1.0 s)

(d) Displacement vs. Time Graph (3 points)

• 1 point for a sinusoidal graph
• 1 point for correct period
• 1 point for correct amplitude

(e) Effect of Tension (3 points)

• 1 point for stating that wave speed increases
• 1 point for stating that wavelength increases
• 1 point for reasonable explanation based on wave speed formula

You've got this! Let's go ace that AP Physics 2 exam! 🎉