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# Discrete Random Variables ## Hypergeometric Distribution (Optional) There are five characteristics of a hypergeometric experiment: 1. You take samples from two groups. 2. You are concerned with a group of interest, called the first group. 3. You sample without replacement from the combined groups. For example, you ...
# Discrete Random Variables ## Poisson Distribution (Optional) There are two main characteristics of a Poisson experiment. 1. The Poisson probability distribution gives the probability of a number of events occurring in a fixed interval of time or space if these events happen with a known average rate and independent...
# Continuous Random Variables ## Introduction Continuous random variables have many applications. Baseball batting averages, IQ scores, the length of time a long-distance telephone call lasts, the amount of money a person carries, the length of time a computer chip lasts, and SAT scores are just a few. The field of r...
# Continuous Random Variables ## Continuous Probability Functions We begin by defining a continuous probability density function. We use the function notation f(x). Intermediate algebra may have been your first formal introduction to functions. In the study of probability, the functions we study are special. We defin...
# Continuous Random Variables ## The Uniform Distribution The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. When working out problems that have a uniform distribution, be careful to note if the data are inclusive or exclusive of endpoints....
# Continuous Random Variables ## The Exponential Distribution (Optional) The exponential distribution is often concerned with the amount of time until some specific event occurs. For example, the amount of time (beginning now) until an earthquake occurs has an exponential distribution. Other examples include the leng...
# The Normal Distribution ## Introduction The normal, a continuous distribution, is the most important of all the distributions. It is widely used and even more widely abused. Its graph is bell-shaped. You see the bell curve in almost all disciplines, including psychology, business, economics, the sciences, nursing, ...
# The Normal Distribution ## The Standard Normal Distribution The standardized normal distribution is a type of normal distribution, with a mean of 0 and standard deviation of 1. It represents a distribution of standardized scores, called , as opposed to raw scores (the actual data values). A indicates the number of...
# The Normal Distribution ## Using the Normal Distribution The shaded area in the following graph indicates the area to the left of x. This area could represent the percentage of students scoring less than a particular grade on a final exam. This area is represented by the probability P(X < x). Normal tables, compute...
# The Central Limit Theorem ## Introduction Why are we so concerned with means? Two reasons are they give us a middle ground for comparison, and they are easy to calculate. In this chapter, you will study means and the central limit theorem. The central limit theorem (clt) is one of the most powerful and useful ideas...
# The Central Limit Theorem ## The Central Limit Theorem for Sample Means (Averages) Suppose X is a random variable with a distribution that may be known or unknown (it can be any distribution). Using a subscript that matches the random variable, suppose 1. = the mean of X 2. = the standard deviation of...
# The Central Limit Theorem ## The Central Limit Theorem for Sums (Optional) Suppose X is a random variable with a distribution that may be known or unknown (it can be any distribution) and suppose: 1. μ = the mean of Χ 2. σ = the standard deviation of X If you draw random samples of size n, then as n increases, the ...
# The Central Limit Theorem ## Using the Central Limit Theorem It is important for you to understand when to use the central limit theorem. If you are being asked to find the probability of the mean, use the clt for the means. If you are being asked to find the probability of a sum or total, use the clt for sums. Thi...
# Confidence Intervals ## Introduction Suppose you were trying to determine the mean rent of a two-bedroom apartment in your town. You might look in the classified section of the newspaper, write down several rents listed, and average them together. You would have obtained a point estimate of the true mean. If you ar...
# Confidence Intervals ## A Single Population Mean Using the Normal Distribution A confidence interval for a population mean with a known standard deviation is based on the fact that the sample means follow an approximately normal distribution. Suppose that our sample has a mean of and we have constructed the ...
# Confidence Intervals ## A Single Population Mean Using the Student's t-Distribution In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this unknown number did not present a problem to statisticians. They used the sample standard deviation s as an estimate for...
# Confidence Intervals ## A Population Proportion During an election year, we see articles in the newspaper that state confidence intervals in terms of proportions or percentages. For example, a poll for a particular candidate running for president might show that the candidate has 40 percent of the vote within 3 per...
# Hypothesis Testing with One Sample ## Introduction One job of a statistician is to make statistical inferences about populations based on samples taken from the population. Confidence intervals are one way to estimate a population parameter. Another way to make a statistical inference is to make a decision about a ...
# Hypothesis Testing with One Sample ## Null and Alternative Hypotheses The actual test begins by considering two hypotheses. They are called the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints. H, the —null hypothesis: a statement of no difference between sample means or ...
# Hypothesis Testing with One Sample ## Outcomes and the Type I and Type II Errors When you perform a hypothesis test, there are four possible outcomes depending on the actual truth, or falseness, of the null hypothesis H and the decision to reject or not. The outcomes are summarized in the following table: The four ...
# Hypothesis Testing with One Sample ## Distribution Needed for Hypothesis Testing Earlier in the course, we discussed sampling distributions. Particular distributions are associated with hypothesis testing. Perform tests of a population mean using a normal distribution or a Student's . (Remember, use a Student's t-d...
# Hypothesis Testing with One Sample ## Rare Events, the Sample, and the Decision and Conclusion Establishing the type of distribution, sample size, and known or unknown standard deviation can help you figure out how to go about a hypothesis test. However, there are several other factors you should consider when work...
# Hypothesis Testing with One Sample ## Additional Information and Full Hypothesis Test Examples 1. In a hypothesis test problem, you may see words such as "the level of significance is 1 percent". The "1 percent" is the preconceived or preset α. 2. The statistician setting up the hypothesis test selects the value of...
# Hypothesis Testing with Two Samples ## Introduction Studies often compare two groups. For example, researchers are interested in the effect aspirin has in preventing heart attacks. Over the last few years, newspapers and magazines have reported various aspirin studies involving two groups. Typically, one group is g...
# Hypothesis Testing with Two Samples ## Two Population Means with Unknown Standard Deviations 1. The two independent samples are simple random samples from two distinct populations. 2. For the two distinct populations The comparison of two population means is very common. A difference between the two samples depe...
# Hypothesis Testing with Two Samples ## Two Population Means with Known Standard Deviations Even though this situation is not likely (knowing the population standard deviations), the following example illustrates hypothesis testing for independent means, known population standard deviations. The sampling distributio...
# Hypothesis Testing with Two Samples ## Comparing Two Independent Population Proportions When conducting a hypothesis test that compares two independent population proportions, the following characteristics should be present: 1. The two independent samples are simple random samples that are independent. 2. The numb...
# Hypothesis Testing with Two Samples ## Matched or Paired Samples (Optional) When using a hypothesis test for matched or paired samples, the following characteristics should be present: 1. Simple random sampling is used. 2. Sample sizes are often small. 3. Two measurements (samples) are drawn from the same pair of i...
# The Chi-Square Distribution ## Introduction Have you ever wondered if lottery numbers were evenly distributed or if some numbers occurred with a greater frequency? How about if the types of movies people preferred were different across different age groups? What about if a coffee machine was dispensing approximatel...
# The Chi-Square Distribution ## Facts About the Chi-Square Distribution The notation for the chi-square distribution is where df = degrees of freedom, which depends on how chi-square is being used. If you want to practice calculating chi-square probabilities then use df = n – –1. The degrees of freedom for the three...
# The Chi-Square Distribution ## Goodness-of-Fit Test In this type of hypothesis test, you determine whether the data fit a particular distribution. For example, you may suspect your unknown data fit a binomial distribution. You use a chi-square test, meaning the distribution for the hypothesis test is chi-square, to...
# The Chi-Square Distribution ## Test of Independence Tests of independence involve using a contingency table of observed (data) values. The test statistic for a test of independence is similar to that of a goodness-of-fit test where 1. O = observed values, 2. E = expected values, 3. i = the number of rows in the tab...
# The Chi-Square Distribution ## Test for Homogeneity The goodness-of-fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to draw a ...
# The Chi-Square Distribution ## Comparison of the Chi-Square Tests You have seen the χ2 test statistic used in three different circumstances. The following bulleted list is a summary that will help you decide which χ2 test is the appropriate one to use. 1. Goodness-of-Fit: Use the goodness-of-fit test to decide whet...
# The Chi-Square Distribution ## Test of a Single Variance A test of a single variance assumes that the underlying distribution is normal. The null and alternative hypotheses are stated in terms of the population variance or population standard deviation. The test statistic is where 1. n = the total number of data, ...
# Linear Regression and Correlation ## Introduction Professionals often want to know how two or more numeric variables are related. For example, is there a relationship between the grade on the second math exam a student takes and the grade on the final exam? If there is a relationship, what is the relationship, and ...
# Linear Regression and Correlation ## Linear Equations Linear regression for two variables is based on a linear equation with one independent variable. The equation has the form where a and b are constant numbers. The variable x is the independent variable; y is the dependent variable. Typically, you choose a value ...
# Linear Regression and Correlation ## The Regression Equation Data rarely fit a straight line exactly. Usually, you must be satisfied with rough predictions. Typically, you have a set of data with a scatter plot that appear to fit a straight line. This is called a line of best fit or least-squares regression line. T...
# Linear Regression and Correlation ## Testing the Significance of the Correlation Coefficient (Optional) The correlation coefficient, r, tells us about the strength and direction of the linear relationship between x and y. However, the reliability of the linear model also depends on how many observed data points are...
# Linear Regression and Correlation ## Prediction (Optional) Recall the third exam/final exam example. We found the equation of the best-fit line for the final exam grade as a function of the grade on the third exam. We can now use the least-squares regression line for prediction. Suppose you want to estimate, or pre...
# Linear Regression and Correlation ## Outliers In some data sets, there are values (observed data points) called outliers. Outliers are observed data points that are far from the least-squares line. They have large errors, where the error or residual is not very close to the best-fit line. Outliers need to be examin...
# F Distribution and One-way Anova ## Introduction Many statistical applications in psychology, social science, business administration, and the natural sciences involve several groups. For example, an environmentalist is interested in knowing if the average amount of pollution varies among several bodies of water. A...
# F Distribution and One-way Anova ## One-Way ANOVA The purpose of a one-way ANOVA test is to determine the existence of a statistically significant difference among several group means. The test uses variances to help determine if the means are equal or not. To perform a one-way ANOVA test, there are five basic assu...
# F Distribution and One-way Anova ## The F Distribution and the F Ratio The distribution used for the hypothesis test is a new one. It is called the , named after Sir Ronald Fisher, an English statistician. The F statistic is a ratio (a fraction). There are two sets of degrees of freedom: one for the numerator and o...
# F Distribution and One-way Anova ## Facts About the F Distribution The following are facts about the F distribution: 1. The curve is not symmetrical but skewed to the right. 2. There is a different curve for each set of dfs. 3. The F statistic is greater than or equal to zero. 4. As the degrees of freedom for the n...
# F Distribution and One-way Anova ## Test of Two Variances Another use of the F distribution is testing two variances. It is often desirable to compare two variances rather than two averages. For instance, college administrators would like two college professors grading exams to have the same variation in their grad...
# What is Physics? ## Introduction Take a look at the image above of the Andromeda Galaxy (), which contains billions of stars. This galaxy is the nearest one to our own galaxy (the Milky Way) but is still a staggering 2.5 million light years from Earth. (A light year is a measurement of the distance light travels in...
# What is Physics? ## Physics: Definitions and Applications ### Section Key Terms ### What Physics Is Think about all of the technological devices that you use on a regular basis. Computers, wireless internet, smart phones, tablets, global positioning system (GPS), MP3 players, and satellite radio might come to m...
# What is Physics? ## The Scientific Methods ### Section Key Terms ### Scientific Methods Scientists often plan and carry out investigations to answer questions about the universe around us. These investigations may lead to natural laws. Such laws are intrinsic to the universe, meaning that humans did not create ...
# What is Physics? ## The Language of Physics: Physical Quantities and Units ### Section Key Terms ### The Role of Units Physicists, like other scientists, make observations and ask basic questions. For example, how big is an object? How much mass does it have? How far did it travel? To answer these questions, th...
# Motion in One Dimension ## Introduction Outside of an airplane, have you ever traveled faster than 150 mph? Can you imagine traveling in a train like the one shown in that goes close to 300 mph? Despite the high speed, the people riding in this train may not notice that they are moving at all unless they look out ...
# Motion in One Dimension ## Relative Motion, Distance, and Displacement ### Section Key Terms ### Defining Motion Our study of physics opens with kinematics—the study of motion without considering its causes. Objects are in motion everywhere you look. Everything from a tennis game to a space-probe flyby of the p...
# Motion in One Dimension ## Speed and Velocity ### Section Key Terms ### Speed There is more to motion than distance and displacement. Questions such as, “How long does a foot race take?” and “What was the runner’s speed?” cannot be answered without an understanding of other concepts. In this section we will loo...
# Motion in One Dimension ## Position vs. Time Graphs ### Section Key Terms ### Graphing Position as a Function of Time A graph, like a picture, is worth a thousand words. Graphs not only contain numerical information, they also reveal relationships between physical quantities. In this section, we will investigat...
# Motion in One Dimension ## Velocity vs. Time Graphs ### Section Key Terms ### Graphing Velocity as a Function of Time Earlier, we examined graphs of position versus time. Now, we are going to build on that information as we look at graphs of velocity vs. time. Velocity is the rate of change of displacement. Acc...
# Acceleration ## Introduction You may have heard the term accelerator, referring to the gas pedal in a car. When the gas pedal is pushed down, the flow of gasoline to the engine increases, which increases the car’s velocity. Pushing on the gas pedal results in acceleration because the velocity of the car increases, ...
# Acceleration ## Acceleration ### Section Key Terms ### Defining Acceleration Throughout this chapter we will use the following terms: time, displacement, velocity, and acceleration. Recall that each of these terms has a designated variable and SI unit of measurement as follows: 1. Time: t, measured in seconds (...
# Acceleration ## Representing Acceleration with Equations and Graphs ### Section Key Terms ### How the Kinematic Equations are Related to Acceleration We are studying concepts related to motion: time, displacement, velocity, and especially acceleration. We are only concerned with motion in one dimension. The kin...
# Forces and Newton’s Laws of Motion ## Introduction Isaac Newton (1642–1727) was a natural philosopher; a great thinker who combined science and philosophy to try to explain the workings of nature on Earth and in the universe. His laws of motion were just one part of the monumental work that has made him legendary. ...
# Forces and Newton’s Laws of Motion ## Force ### Section Key Terms ### Defining Force and Dynamics Force is the cause of motion, and motion draws our attention. Motion itself can be beautiful, such as a dolphin jumping out of the water, the flight of a bird, or the orbit of a satellite. The study of motion is ca...
# Forces and Newton’s Laws of Motion ## Newton's First Law of Motion: Inertia ### Section Key Terms ### Newton’s First Law and Friction Newton’s first law of motion states the following: 1. A body at rest tends to remain at rest. 2. A body in motion tends to remain in motion at a constant velocity unless acted on...
# Forces and Newton’s Laws of Motion ## Newton's Second Law of Motion ### Section Key Terms ### Describing Newton’s Second Law of Motion Newton’s first law considered bodies at rest or bodies in motion at a constant velocity. The other state of motion to consider is when an object is moving with a changing veloci...
# Forces and Newton’s Laws of Motion ## Newton's Third Law of Motion ### Section Key Terms ### Describing Newton’s Third Law of Motion If you have ever stubbed your toe, you have noticed that although your toe initiates the impact, the surface that you stub it on exerts a force back on your toe. Although the firs...
# Motion in Two Dimensions ## Introduction In Chapter 2, we learned to distinguish between vectors and scalars; the difference being that a vector has magnitude and direction, whereas a scalar has only magnitude and possibly sign. We learned how to deal with vectors in physics by working straightforward one-dimension...
# Motion in Two Dimensions ## Vector Addition and Subtraction: Graphical Methods ### Section Key Terms ### The Graphical Method of Vector Addition and Subtraction Recall that a vector is a quantity that has magnitude and direction. For example, displacement, velocity, acceleration, and force are all vectors. In o...
# Motion in Two Dimensions ## Vector Addition and Subtraction: Analytical Methods ### Section Key Terms ### Components of Vectors For the analytical method of vector addition and subtraction, we use some simple geometry and trigonometry, instead of using a ruler and protractor as we did for graphical methods. How...
# Motion in Two Dimensions ## Projectile Motion ### Section Key Terms ### Properties of Projectile Motion Projectile motion is the motion of an object thrown (projected) into the air when, after the initial force that launches the object, air resistance is negligible and the only other force that object experienc...
# Motion in Two Dimensions ## Inclined Planes ### Section Key Terms ### Static Friction and Kinetic Friction Recall from the previous chapter that friction is a force that opposes relative motion parallel to the contact surface of the interacting objects and is around us all the time. Friction allows us to move, ...
# Motion in Two Dimensions ## Simple Harmonic Motion ### Section Key Terms ### Hooke’s Law and Simple Harmonic Motion Imagine a car parked against a wall. If a bulldozer pushes the car into the wall, the car will not move but it will noticeably change shape. A change in shape due to the application of a force is ...
# Circular and Rotational Motion ## Introduction You may recall learning about various aspects of motion along a straight line: kinematics (where we learned about displacement, velocity, and acceleration), projectile motion (a special case of two-dimensional kinematics), force, and Newton’s laws of motion. In some wa...
# Circular and Rotational Motion ## Angle of Rotation and Angular Velocity ### Section Key Terms ### Angle of Rotation What exactly do we mean by circular motion or rotation? Rotational motion is the circular motion of an object about an axis of rotation. We will discuss specifically circular motion and spin. Cir...
# Circular and Rotational Motion ## Uniform Circular Motion ### Section Key Terms ### Centripetal Acceleration In the previous section, we defined circular motion. The simplest case of circular motion is uniform circular motion, where an object travels a circular path at a constant speed. Note that, unlike speed,...
# Circular and Rotational Motion ## Rotational Motion ### Section Key Terms ### Rotational Kinematics In the section on uniform circular motion, we discussed motion in a circle at constant speed and, therefore, constant angular velocity. However, there are times when angular velocity is not constant—rotational mo...
# Newton's Law of Gravitation ## Introduction What do a falling apple and the orbit of the moon have in common? You will learn in this chapter that each is caused by gravitational force. The motion of all celestial objects, in fact, is determined by the gravitational force, which depends on their mass and separation....
# Newton's Law of Gravitation ## Kepler's Laws of Planetary Motion ### Section Key Terms ### Concepts Related to Kepler’s Laws of Planetary Motion Examples of orbits abound. Hundreds of artificial satellites orbit Earth together with thousands of pieces of debris. The moon’s orbit around Earth has intrigued human...
# Newton's Law of Gravitation ## Newton's Law of Universal Gravitation and Einstein's Theory of General Relativity ### Section Key Terms ### Concepts Related to Newton’s Law of Universal Gravitation Sir Isaac Newton was the first scientist to precisely define the gravitational force, and to show that it could exp...
# Momentum ## Introduction We know from everyday use of the word momentum that it is a tendency to continue on course in the same direction. Newscasters speak of sports teams or politicians gaining, losing, or maintaining the momentum to win. As we learned when studying about inertia, which is Newton's first law of m...
# Momentum ## Linear Momentum, Force, and Impulse ### Section Key Terms ### Momentum, Impulse, and the Impulse-Momentum Theorem Linear momentum is the product of a system’s mass and its velocity. In equation form, linear momentum p is You can see from the equation that momentum is directly proportional to the obj...
# Momentum ## Conservation of Momentum ### Section Key Terms ### Conservation of Momentum It is important we realize that momentum is conserved during collisions, explosions, and other events involving objects in motion. To say that a quantity is conserved means that it is constant throughout the event. In the ca...
# Momentum ## Elastic and Inelastic Collisions ### Section Key Terms ### Elastic and Inelastic Collisions When objects collide, they can either stick together or bounce off one another, remaining separate. In this section, we’ll cover these two different types of collisions, first in one dimension and then in two...
# Work, Energy, and Simple Machines ## Introduction Roller coasters have provided thrills for daring riders around the world since the nineteenth century. Inventors of roller coasters used simple physics to build the earliest examples using railroad tracks on mountainsides and old mines. Modern roller coaster designe...
# Work, Energy, and Simple Machines ## Work, Power, and the Work–Energy Theorem ### Section Key Terms ### The Work–Energy Theorem In physics, the term work has a very specific definition. Work is application of force, , to move an object over a distance, d, in the direction that the force is applied. Work, W, is...
# Work, Energy, and Simple Machines ## Mechanical Energy and Conservation of Energy ### Section Key Terms ### Mechanical Energy and Conservation of Energy We saw earlier that mechanical energy can be either potential or kinetic. In this section we will see how energy is transformed from one of these forms to the ...
# Work, Energy, and Simple Machines ## Simple Machines ### Section Key Terms ### Simple Machines Simple machines make work easier, but they do not decrease the amount of work you have to do. Why can’t simple machines change the amount of work that you do? Recall that in closed systems the total amount of energy i...
# Special Relativity ## Introduction Have you ever dreamed of traveling to other planets in faraway star systems? The trip might seem possible by traveling fast enough, but you will read in this chapter why it is not. In 1905, Albert Einstein developed the theory of special relativity. Einstein developed the theory t...
# Special Relativity ## Postulates of Special Relativity ### Section Key Terms ### Scientific Experiments and Problems Relativity is not new. Way back around the year 1600, Galileo explained that motion is relative. Wherever you happen to be, it seems like you are at a fixed point and that everything moves with r...
# Special Relativity ## Consequences of Special Relativity ### Section Key Terms ### Relativistic Effects on Time, Distance, and Momentum Consideration of the measurement of elapsed time and simultaneity leads to an important relativistic effect. Time dilation is the phenomenon of time passing more slowly for an ...
# Thermal Energy, Heat, and Work ## Introduction Heat is something familiar to all of us. We feel the warmth of the summer sun, the hot vapor rising up out of a cup of hot cocoa, and the cooling effect of our sweat. When we feel warmth, it means that heat is transferring energy to our bodies; when we feel cold, that ...
# Thermal Energy, Heat, and Work ## Temperature and Thermal Energy ### Section Key Terms ### Temperature What is temperature? It’s one of those concepts so ingrained in our everyday lives that, although we know what it means intuitively, it can be hard to define. It is tempting to say that temperature measures he...
# Thermal Energy, Heat, and Work ## Heat, Specific Heat, and Heat Transfer ### Section Key Terms ### Heat Transfer, Specific Heat, and Heat Capacity We learned in the previous section that temperature is proportional to the average kinetic energy of atoms and molecules in a substance, and that the average interna...
# Thermal Energy, Heat, and Work ## Phase Change and Latent Heat ### Section Key Terms ### Phase Changes So far, we have learned that adding thermal energy by heat increases the temperature of a substance. But surprisingly, there are situations where adding energy does not change the temperature of a substance at...
# Thermodynamics ## Introduction Energy can be transferred to or from a system, either through a temperature difference between it and another system (i.e., by heat) or by exerting a force through a distance (work). In these ways, energy can be converted into other forms of energy in other systems. For example, a car...
# Thermodynamics ## Zeroth Law of Thermodynamics: Thermal Equilibrium ### Section Key Terms We learned in the previous chapter that when two objects (or systems) are in contact with one another, heat will transfer thermal energy from the object at higher temperature to the one at lower temperature until they both r...
# Thermodynamics ## First law of Thermodynamics: Thermal Energy and Work ### Section Key Terms ### Pressure, Volume, Temperature, and the Ideal Gas Law Before covering the first law of thermodynamics, it is first important to understand the relationship between pressure, volume, and temperature. Pressure, P, is d...
# Thermodynamics ## Second Law of Thermodynamics: Entropy ### Section Key Terms ### Entropy Recall from the chapter introduction that it is not even theoretically possible for engines to be 100 percent efficient. This phenomenon is explained by the second law of thermodynamics, which relies on a concept known as ...
# Thermodynamics ## Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators ### Section Key Terms ### Heat Engines, Heat Pumps, and Refrigerators In this section, we’ll explore how heat engines, heat pumps, and refrigerators operate in terms of the laws of thermodynamics. One of the most impor...
# Waves and Their Properties ## Introduction Recall from the chapter on Motion in Two Dimensions that oscillations—the back-and-forth movement between two points—involve force and energy. Some oscillations create waves, such as the sound waves created by plucking a guitar string. Other examples of waves include earth...
# Waves and Their Properties ## Types of Waves ### Section Key Terms ### Mechanical Waves What do we mean when we say something is a wave? A wave is a disturbance that travels or propagates from the place where it was created. Waves transfer energy from one place to another, but they do not necessarily transfer a...
# Waves and Their Properties ## Wave Properties: Speed, Amplitude, Frequency, and Period ### Section Key Terms ### Wave Variables In the chapter on motion in two dimensions, we defined the following variables to describe harmonic motion: 1. Amplitude—maximum displacement from the equilibrium position of an object...
# Waves and Their Properties ## Wave Interaction: Superposition and Interference ### Section Key Terms ### Superposition of Waves Most waves do not look very simple. They look more like the waves in , rather than the simple water wave considered in the previous sections, which has a perfect sinusoidal shape. Most...