Notes for Waves and Resonance

Waves are the main topic for both, but resonance is only for the experiment validation test, so they’ll be in that order. Both are to be completed within 50 minutes in class during Period 5 of Wednesday.

I’ll be honest this is the first time I’m a bit unsure of where the line is drawn between these two. The revision checklist is there but I’m pretty sure resonance is only for the validation. The experiment itself was also interference phenomena, such as sound waves inside of closed pipes and finding resonant lengths for certain frequencies, but that’s in the revision checklist as well. Of course, (in Dr Water’s class) we did standing waves and some interference phenomena involving nodal lines and such, but that was it in terms of the topic test.

Topic Test - Waves

Waves will be the focus of the test. The objectives for this topic test in the form of a checklist is on Connect and can be found on this notice. The general topics are explained below.

Summary

1. Waves and Classifications
2. Wave equations and anatomy
3. Graphing Waves/Analysis of waves
4. Reflection and Refraction
5. Standing Waves
6. Interference phenomena

Waves and Classifications

A wave is a disturbance with periodic oscillations that transfers energy from its origin to another point. When waves move through space, they can displace particles, however, the net displacement of these particles is 0/there is no net transfer of matter. There are a few misconceptions about this, so take note of the common misconceptions below:

1. There is no matter displaced: X –> Matter is displaced, but particles will return to their original position ceteris paribus (haha econoemik gags moment, this kind of answer really isn’t needed unless a question presses for it, otherwise just say what is above)
2. No matter cannot be net displaced by the energy a wave transfers: X –> Take for example a surfer surfing on a wave on the ocean (an actual wave!). Only the particles in the medium (water) that the wave is travelling in experiences no net displacement, however, the surfer is most definitely displaced (I mean that’s surfing… unless you don’t know what surfing is, in that case, have a bit of time outside on God’s green Earth (I’m not Christian or Christian))

Waves can be classified into four different categories based on their properties, which are transverse, longitudinal, mechanical and non-mechanical. Transverse waves oscillate, and hence, displace matter perpendicularly to their own direction/propagation. Longitudinal waves, on the other hand, displaces matter in the same direction that they move, that is, the direction of the displacement of particles is parallel to the direction of the wave’s propagation. Mechanical waves require a medium (usually a substance constituting of some type of matter) to travel, while non-mechanical waves do not require a medium to travel (but can still travel through most media (plural of medium, keep in mind, but haha how’s it going in the news guys maybe news is a type of wave who knows)). Below is a cross-table with some examples of these types of waves.

	Transverse	Longitudinal
Mechanical	Water/ocean wave	Sound
Non-mechanical	Electromagnetic radiation	Electromagnetic radiation 1

Waves equations and anatomy

Waves have multiple features that allow for distinguishing between different types. The following are all such features: wavelength, frequency, amplitude, period and velocity.

The wavelength of a wave ($\lambda$) is the distance between a whole wave cycle, which is the spacial repetition (or two recurring points on the graph of a wave, though that’s further ahead). Because waves have periodic (and hence, (also further ahead) using the equations, frequent), a wave will always have a set wavelength (except when propagating through different media or interactions with other waves). Wavelength is typically measured in metres.

The frequency ($f$) of a wave refers to how many wave cycles occur within one second. The frequency of a wave is a conserved quantity in the sense that it will not change regardless of entering new media or interacting with other waves. Frequencies are also one characteristic of a wave that affects the amount of energy it carries. Since the energy it carries is essentially the total mechanical energy (sum of kinetic energy (which includes velocity of which frequency is a factor of, also ahead) and potential energy), velocity of the wave is a factor of it (which frequency contributes to).

The amplitude ($\text{A}$) of a wave depicts the change in distance/displacement/pressure of particles that the waves encounters in relative to their original position/pressure. This is shown in graphs as the difference of y-value of points on the graph from the rest position to a crest/trough (with corresponding axes).

The period ($\text{T}$) of a wave is the amount of time it takes for one wave cycle to complete, usually measured in seconds. This, as you may know, seems like the opposite of frequency, and it is known as the inverse/reciprocal of frequency.

The velocity ($\text{v}$) of a wave is

Graphing Waves/Analysis of Waves

Waves can be graphed to depict, essentially, the magnitude of their features. These features include

Footnotes