Exam Coverage

The good sis David posted up the coverage for the exam on the syllabus.


I want to die


For this study guide, I will be using the following resources:


Superposition & Standing Waves

Honestly, I did not attend class for this stuff, which is mostly why I am making this study guide. I love being so extra that I am making this study guide in RStudio! ~dead emoji~

When we look at a standing wave, we usually look at a string because this is not university physics and strings are very useful tools I guess? This means that we have to understand certain properties of waves.

All waves have a frequency, which is the rate of vibration measured in Hz. This is derived from the period, which is the amount of time it takes for a wave to complete one full oscillation. A period is measured in seconds, and this is pretty basic but I always forget about it.


\(f=\frac{1}{T}\)

\(T=\frac{seconds}{n}\)


This second equation is kind of confusing and it only really made sense to me in lab. n is the number of nodes/modes (which the textbook and MasteringPhysics uses interchangeably with m and modes), which you can count as the number of peaks (or troughs) in a wave function.

Waves also have a wavelength, which is defined as the distance between two peaks of a wave; it is measured in meters although we often see it in cm. MasteringPhysics usually cares about conversions, but I do not think David is the same way. From wavelength, we can determine the speed of the wave, which is just v measured in m/s. You could divide the wavelength by the period, but it is usually easier for these problems to multiply by the frequency because it is the inverse of the period. Here are three equations that we can get from the relationship between speed, time, and distance:


\(v=\lambda f\;\;\) \(\frac{v}{\lambda} = f\;\;\) \(\frac{v}{f} = \lambda\;\;\)


Remember these I guess?

A concept that was introduced in lab, that I feel like Hoogewerff made no real mention of (or maybe I just wasn’t paying attention lol sorry) was the length (L) of a string. Apparently, the length of the string multiplied by 2 is the wavelength of the standing wave in the string.


\(\lambda = 2L\)


We can also substitute this value into the equation for frequency: \(f=\frac{v}{2L}\). Nice!

This stuff is pretty much review because we’ve been working with waves forever, but I feel like a lot of physics is just reviewing and reviewing the same old stuff that we’ve done before but just putting different terms and concepts to it.

If we want to relate velocity to the length of a string, we must use an equation that is really ugly and annoying and I hate it. For some reason, it requires the linear density of a string and the tension of a string, which is so extra?


\(v=\sqrt{\frac{T}{\frac{m}{L}}}\)


Linear density, which can be abbreviated as \(\mu\), is some dumb value that we get by dividing the mass of the string (which is usually in grams so must be converted to kilograms) and the length of the string (which is usually in centimeters and must be converted to meters). Usually the velocity is the unknown when we are given problems using this equation, but sometimes the writers of problems like to be annoying and ask about the values under the radical. Thanks for showing me who a fake friend look like.

Now, I think we should look at resonance and harmonics. Cool stuff right??? This is where the number of peaks/modes/nodes/etc. comes into play. To find the frequency at a certain number of harmonics, we must use n in the equation to find frequency.


\(f_n=\frac{nv}{2L}\)


This is basically the same equation as the relationship between velocity, wavelength, and frequency but after she went out and focused on her career and dropped her toxic relationships.

Another similar relationship is the one between resonant frequency (prolly not the right term but ~shrug emoji~) and fundamental frequency.


\(f_n=fn\) therefore \(\frac{f_n}{n}=f\)


Apparently there is also a simple way of subtracting two frequencies, but I only heard that vaguely in lab and I think this one is more applicable when you are given a more simple harmonic.

Here is a graphical relationship between velocity, length, and frequency from our textbook.



David likes to do multiple choice questions about relationships like this, so remember that as frequency increases, velocity increases; as frequency increases length (related to \(\lambda\)) decreases.

There’s also some other ugly conceptual stuff that I want to include but never really understood.

Apparently, superposition is defined as:


when two or more waves a simultaneously present at a single point in space…is the sum of the displacements due to the individual wave


That makes a whole lot of sense…

Furthermore, interference can be constructive or destructive. When the overlap of displacement is larger than both of the waves separately, interference is constructive; when the overlap of displacement is smaller than both of the waves separately, interference is destructive.


Wave Optics

God, I hate this and I want to die.

We only have one section in chapter 17 and this is called “What is light?” like okay do you really think I care what light is?

Anyways, light can be viewed through the wave model, the ray model, and the photon model. Wave model views light as a wave (cool), ray model views lights as a straight line (basis for chapter 18), and photon model views light as a quanta with both wavelike and particulate behavior (thanks gen chem I).



I just feel like David wants us to see this to understand the power of barriers

Oh fuck, now that I’m looking at this section it actually goes more in depth than I expected. It seemed really irrelevant, but this is where the index of refraction is introduced, which is the ratio between the speed of light in a vacuum and the speed of light in a specific material.


\(n=\frac{c}{v}\)


Why is everything abbrieviated with n in this class?

Also, I could have used this equation when I was doing the problems but I hate using the textbook so I ignored it.


\(\lambda_{material}=\frac{\lambda_{vacuum}}{n}\)


Some useful definitions:

diffration: the spreading of a wave (which in this case we could consider it as it passes through a barrier) refraction: a wave being deflected through a medium (hencem index of refraction)


Ray Optics

In this section, the ray model of light is studied in greater depth, even though I feel like the photon model is superior. But anyways, the ray model of light uses the trig that I guess is the basis of a non-calculus based physics. Yay.

We need to understand the concept of reflection because light rays are reflected.

Rays are continuous vectors that travel forever unless they interact with a material. Rays can be reflected off of a material or refracted and travel through a material (which is where we use the index of refraction). Light rays can be both reflected and refracted. Light can also be scattered or absorbed within a material, but I don’t really care about that.

Note: shadows occur when an opaque object interferes with the source of a light ray. It’s not that deep and I doubt it will be on David’s exam. Shadows occur when light is refracted through an object with a much lower n value.

Specular reflection occurs when rays of light are reflected from “smooth, shiny surfaces” which in the scope of our course is just a mirror. This figure contains the important parts of specular reflection: incident and reflected rays with their corresponding angles over the surface with a hypothetical normal line dividing the trajectories of the two rays.



The law of reflection states that \(\theta_{r} = \theta_{i}\) which is sort of irrelevant because most of our calculations come from Snell’s law, but I guess this is helpful anyway. Also, note that the normal is the angle between the ray and the normal, and not the angle between the surface and the ray.

Because we are discussing the reflection of light, the concept of images are also important to consider. Images can be real or virtual. A real image occurs when the image is produced from where the light rays actually converge. A virtual image occurs when the image is produced from a point where light rays diverge.

When we discuss the refraction of light, we can use indexes of refraction to create a mathematical relationship between the angles of refraction as light travels through a surface. Remember that the angle is measured between the normal and the ray. Snell’s law outlines this ratio.


Snell’s law: \(n_{1} sin\theta_{1} = n_{2} sin\theta_{2}\)


For reference, here are some indexes of refraction. (David will prolly give them out on the exam)



Now is the worst part of this chapter: tracing rays through lenses, which is the single concept that made me hate light as a phenomenon in our universe.

When constructing a ray tracing diagram, we must include the three principal rays to make David happy because this is a concept I believe will be on our exam as part of a problem (in the way that he gives a problem and then says we must draw a force diagram). These principal rays are:




The kinds of rays we look at in the scope of this class travel through two types of lenses: concave (converging) and convex (diverging). When a lens is concave, the rays converge at the far focal point. These sort of lenses can produce a real image when an object is located beyond the near focal point, but can also produce virtual images if the object is before the focal point. When a lens is convex, the rays refract through the mirror and reflect back through to an a point where a virtual image is created. These lenses can only produce virtual images.



Objects that are reflected/refracted through mirrors/lenses naturally have heights. They also have an individual distance from the mirror/lens. We can also consider the distance of the focal point, which is true to both the far and near focal lengths.

We must consider the relationship betweeen the object/image distances and their heights. Height and distance are related through a ratio we can define as:


\(\frac{h_{i}}{h_{o}}=\frac{d_{i}}{d_{o}}\)


We can relate this ratio to magnifaction, which is given as:


\(m=-\frac{d_{i}}{d_{o}}\)


Does it make sense? Not quite, but just remember that if the magnification is negative, then the image is inverted and if it is positive it is upright. Cool I guess? \(\mid{m}\mid\) = the ratio of the height of the objects; since height cannot truly be negative, the absolute value is the irl height.

Now that we’ve introduced the concept of ray tracing and the types of lenses, we can look at the thin-lens equation.

Important to remember that the focal length of a converging lens is positive, and the focal length of a diverging lens is negative.

The thin-lens equation is derived from some mathematical bullshit, but all we really need to know is the actual equation so we can do the calculations correctly. Here it is, quite simple math albeit ugly:


\(\frac{1}{d_0}+\frac{1}{d_i}=\frac{1}{f}\)


That’s pretty much all we need for this chapter. And onto the one that I clocked out the most during…


Electric Fields and Forces

The electromagnetic force is one of the fundamental forces of the physical universe.


Basics of charge:


That’s that on that.

Conductors are objects that easily transfer charge, while insulators prevent charge from changing.

Charges in a neutral object can become polarized when in close proximity with a net positive/negative charge.

Charges come from the structure of the atom, which contains submicroscopic particles known as protons, electrons, and neutrons. Protons and neutrons are about equal in mass, with electron mass being much smaller. Neutrons carry no net charge, while protons and electrons carry equal and oppositve elementary charges.



Coloumb’s law is the mathematical equation that we can use to determine the electrostatic force between two charges. This law relates to the distance, charges, and the electrostatic constant, which is reminiscent of the force between two objects ignoring gravity.


\(F=\frac{k\mid q_1 \mid \mid q_2 \mid}{r^2}\)


This force is measured in Newton’s per Coloumb, and it is a vector so it can have both x and y components. Use trig to determine the x and y components of these forces to determine the net electromagnetic force exerted between two or more charges.

Now, we can look at the field model of electric charges, which states that a point charge alters the space around an object, which is visualized for ease as a vector, but is very squiggly (because it constitutes all free space in that particular radius) when we look at it in the theoretical visualization.



This is a vector, so again we can use trig to determine the x and y components of this model. We can sum the x and y components and then use the Pythagorean theorem to determine the true magnitude of the electric field.

Negative charges have electric fields that point towards the point charge whereas positive charges have electric charges that point away from the point charge. We can visualize this like so:

The equation to determine the magnitude of an electric field is quite simple. It is the electric force divided by the radius (distance) of between the point charge and the electric field.


\(E=\frac{k\mid q \mid}{r^2}\)


I don’t really see how it’s different from the electric force equation but okay werk.

Here is the graphical relationship between electric field magnitude versus radius length.



This is not on our equation list and I was not in class, but apparently the electric field of a capacitor is:


\(E=\frac{Q}{\epsilon_{0}A}\)


Which requires the charge (Q) to area (A) ratio multiplied by the permittivity constant given on our formula sheet. I did ntot use this one on the homework nor was I in class to see if David used it but there’s that in case it shows up. E and Q are directly proprtional in this relationship. Cool.

Here is a dipole which looks really pretty. I don’t think we need to know it, but a dipole consists of negative and positive charges separated by a distance. Water is the most basic example of a dipole I can think of.



Also, our textbook says this: “the electric field is 0 at all points in a conductor in electrostatic equilibrium.” Excess charge lies at the surface. I don’t think he’ll go in depth on this section.


Here is some other stuff that I don’t really understand.

To find tension, we must know both the gravitational force and the electrostatic (electromagnetic force? I have no clue). I don’t remember David going over this in class, and we are so far behind in lab, and I feel like it is not in the textbook. So like yeah. This is the equation:

\(T=mg+Eq\)

I might come back and add some practice problems but idk I just wanna die