#AP Physics 2: Waves - Your Last Minute Guide 🚀

Hey there, future physicist! Let's get you prepped for the AP Physics 2 exam with a super-focused review of waves. Remember, it's all about understanding the concepts and how they connect. Let's dive in!

#Introduction to Waves

Waves are all about energy transfer without moving matter. Think of it like a ripple in a pond – the water doesn't travel across the pond, but the energy does! Let's break it down:

• Energy Transfer: Waves move energy from one place to another. No matter is transferred, just the energy. 🌊
• Wave Pulse: A single disturbance that carries energy. Think of a quick flick of a rope.
• Continuous Waves: Periodic disturbances with specific wavelengths and frequencies. These are the waves we usually think about (like sound or light).

#Types of Waves

Let's explore the different types of waves:

#Mechanical vs. Electromagnetic Waves

• Mechanical Waves: Need a medium (like air, water, or a string) to travel through. Examples include sound waves and waves on a string.
• Electromagnetic Waves: Don't need a medium; they can travel through a vacuum. Examples include light, radio waves, and X-rays.

#Transverse vs. Longitudinal Waves

• Transverse Waves: The disturbance is perpendicular to the direction the wave travels. Think of a wave on a string or light waves.
• Longitudinal Waves: The disturbance is parallel to the direction the wave travels. Sound waves are a classic example. 🔊

Transverse Wave (left) and Longitudinal Wave (right)

#Wave Properties

Understanding these properties is key to mastering waves:

#Wave Speed

• General: Wave speed depends on the wave type and the medium it's traveling through.
• Electromagnetic Waves in Vacuum: All travel at the speed of light: $c = 3.00 \times 10^8 \text{ m/s}$.
• Waves on a String: The speed depends on the tension ($F_T$) and mass per unit length ($m/\ell$):

$$v_{\text{string}} = \sqrt{\frac{F_T}{m/\ell}}$$

• Sound Waves: Speed increases with temperature in a given medium.

#

• Definition: The maximum displacement of a wave from its equilibrium position.
• Longitudinal Waves: Amplitude is the maximum pressure change from equilibrium.
• Loudness: Higher amplitude means louder sound. 📈
• Energy: Higher amplitude waves carry more energy. 💡

Amplitude (A) is the maximum displacement of the wave.

#Final Exam Focus

Okay, let's focus on what's most important for the exam:

• Wave Types: Know the difference between mechanical/electromagnetic and transverse/longitudinal waves.
• Wave Speed: Understand how wave speed is affected by the medium and the specific formulas for strings and electromagnetic waves.
• Amplitude and Energy: Remember that amplitude is directly related to the energy a wave carries.

#

• Units: Always double-check your units! Make sure they match up in your calculations.
• Formulas: Know the key formulas and when to apply them.
• Conceptual Understanding: Don't just memorize equations; understand the underlying concepts.
• Time Management: Don't get stuck on one question. Move on and come back if you have time.

#

• Mixing Up Wave Types: Be careful not to confuse transverse and longitudinal waves.
• Incorrect Formulas: Double-check you're using the correct formula for the situation.
• Forgetting Units: Always include units in your answers.

#Practice Questions

Practice Question

#Multiple Choice Questions

1. A wave travels through a medium. Which of the following properties of the wave is NOT affected by a change in the medium? (A) Speed (B) Wavelength (C) Frequency (D) Amplitude

2. A string with a mass per unit length of 0.02 kg/m is under a tension of 200 N. What is the speed of a wave on the string? (A) 10 m/s (B) 100 m/s (C) 141 m/s (D) 200 m/s

3. Which of the following is an example of a longitudinal wave? (A) Light wave (B) Radio wave (C) Sound wave (D) Water wave

#Free Response Question

A string is stretched between two fixed points. The string has a length of 2.0 m and a mass of 0.04 kg. The tension in the string is 100 N.

(a) Calculate the speed of a wave on the string. (2 points)

(b) If a wave with a frequency of 50 Hz is generated on the string, what is the wavelength of the wave? (2 points)

(c) If the tension in the string is increased, how will the speed of the wave change? Explain your reasoning. (2 points)

(d) If the mass per unit length of the string is increased, how will the speed of the wave change? Explain your reasoning. (2 points)

#Answer Key & Scoring Breakdown

Multiple Choice:

1. (C) Frequency
2. (B) 100 m/s
3. (C) Sound wave

Free Response:

(a) Speed of the wave:

$$v = \sqrt{\frac{F_T}{m/\ell}} = \sqrt{\frac{100 N}{0.04 kg / 2.0 m}} = \sqrt{\frac{100}{0.02}} = \sqrt{5000} = 70.7 \text{ m/s}$$

• 1 point for using the correct formula.
• 1 point for correct calculation and answer.

(b) Wavelength of the wave:

$$v = f \lambda \Rightarrow \lambda = \frac{v}{f} = \frac{70.7 \text{ m/s}}{50 \text{ Hz}} = 1.41 \text{ m}$$

• 1 point for using the correct formula.
• 1 point for correct calculation and answer.

(c) If the tension is increased, the speed of the wave will increase. The speed of the wave is directly proportional to the square root of the tension, as shown by the equation $v = \sqrt{\frac{F_T}{m/\ell}}$. (2 points)

• 1 point for stating the speed will increase.
• 1 point for correct reasoning.

(d) If the mass per unit length is increased, the speed of the wave will decrease. The speed of the wave is inversely proportional to the square root of the mass per unit length, as shown by the equation $v = \sqrt{\frac{F_T}{m/\ell}}$. (2 points)

• 1 point for stating the speed will decrease.
• 1 point for correct reasoning.

#Wrapping Up

You've got this! Remember to stay calm, trust your preparation, and tackle each question methodically. You're ready to rock this exam! 🎉