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Unit 6

# 6.1 Waves 🌊

Saarah Hasan Caroline Koffke

### AP Physics 2🧲

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## Unit 6: Geometric and Physical Optics

### 6.0: Overview

Waves! If you’ve taken AP Physics 1, chances are that you’re pretty familiar with the subject. In Physics 2, Unit 6 focuses on electromagnetic waves, primarily light (which, yes, is technically considered both a wave and a particle). For this unit, we’ll mainly explore the different ways light can be thought about and modeled.

### 6.1: Waves🌊

What is a wave? Well, in simple terms, a wave can be described as a disturbance that carries energy through a medium—the substance/material that carries the wave—from one place to another. Waves transfer energy without transferring matter; energy moves from place to place, yet the particles of matter in the medium return to their original location.
Let’s take a look at this in a real-life example.
Imagine a stadium wave. Each person in the audience stands up and then quickly sits back down to make the wave. The disturbance travels through the stadium, but the people in the audience don’t move from where their seat is. They don’t walk around the stadium to make the wave.

Properties of Waves:

While all waves share some basic properties, they can come in different shapes and forms. It’s common to categorize waves based on certain characteristics:
• Transverse Wave—A wave in which particles of the medium move in a direction perpendicular to the motion of the wave.
• Longitudinal Wave—A wave in which particles of the medium move parallel to the motion of the wave.
• Mechanical Wave—A wave that isn’t capable of transmitting its energy through a vacuum; mechanical waves require a medium to travel and can be both longitudinal or transverse.
• Electromagnetic Wave—A wave that’s capable of transmitting its energy through a vacuum; electromagnetic waves are produced by the vibrations of charged particles and are always transverse.

Anatomy of Waves:

Let’s take a closer look at the parts of waves.🔎
Transverse Waves: Taken from Wikimedia Commons

Longitudinal Waves: Taken from Wikimedia Commons

• Wavelength (λ)—The distance/length of the wave measured from two identical points, from crest to crest or from trough to trough; it’s the length of one complete wave cycle.
• Amplitude (a)—The height of the wave or distance from rest to max. displacement. Amplitude is proportional to the amount of energy carried by a wave: a high energy wave has a high amplitude; a low energy wave has a low wave.
• Crest—The point on a wave where the amount of positive/upward displacement from rest is at a max.
• Trough—The point on a wave where the amount of negative/downward displacement from rest is at a max.
• Compression—A region in a longitudinal wave where the particles are closest together (max. density).
• Rarefaction—A region in a longitudinal wave where the particles are farthest apart (min. density).
• Frequency (f)—The number of waves made per second; measured in Hertz (Hz)
• Period (T)—The amount of time it takes to make one wave; measured in seconds (s).

Wave Equations:

👇Let’s jot down the formulas/equations we’ll need to solve wave-related physics problems.👇
T=1/f ﻿ f=1/T﻿
The frequency is the reciprocal of the period and vice versa.
speed=distance/time
For waves, the speed is the distance traveled by a point (like the crest/trough) on the wave over a given amount of time. In the time of one period, a wave moves the distance of one wavelength. So from that, we can say:
Speed=Wavelength/Period ➡️ v=λ/Tv=λ/T﻿
Speed=Wavelength*Frequency ➡️ v=λ*fv=λf﻿
While wave speed is calculated by multiplying frequency and wavelength, changing either of the two doesn’t affect wave speed. The speed of a wave depends upon the medium in which the wave travels.
Check out this interactive to explore this concept further.

Practice Problems:🧩

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

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, like all waves when traveling between two mediums, the frequency remains constant. Based on v = f λ, if the speed decreases and the frequency is constant then the λ must decrease also.

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