Waves - LeFonch

What are Waves?

A wave is a movement of energy, as energy travels from one place to another.
Thus a wave that makes energy travel is called a "travelling wave".
The transfer of energy by waves is called the propagation of waves.

Mechanical waves rely on the movement of particles, and thus require a substance to pass through in order to exist.
This is called the medium of the wave.
This is also why mechanical waves cannot occur in a vacuum, as there is no medium for them to travel through.
For example, you cannot hear sound in space, as there is no medium for sound waves to travel through.

You can imagine mechanical waves as transfer of energy through collisions for example, except now there are millions of tiny particles instead of just one or two bodies.
As they all bump into one another, they transfer their energy, causing the wave to move forward.

In a transverse wave, particles oscillate up and down, creating a motion that looks like wave.
Imagine a singular particle going up and down, like how a person in their seat can sit down and raise their hands.
On its own it doesn't look like much, but when a lot of particles are moving in unison, then it starts to look like a wave, just like how a bunch of people raising their hands in a stadium looks like a big wave!
This tiny particle, and thus all the particles together, are moving in simple harmonic motion!

In longitudinal waves, the oscillation is along the wave, which means that particles move back and forth.
Imagine a singular particle moving back and forth.
On its own it doesn't look like much, but when a bunch of particles are moving back and forth together, it starts to look like a wave!
Just like transverse waves, each particle is moving in simple harmonic motion.

Displacement is parallel to the direction of the wave.
Areas where particles are densely packed together is called a compression, and areas where particles are less tightly packed is called a rarefaction.
Compressions occur when a particle's displacement is the highest, as many particles move away from their equilibrium point and meet up at the compression ahead.
It is similar to a maximum points in transverse waves.
Rarefactions occur when displacement of a particle is the lowest, as particles move away from their equilibrium and meet up at the compression behind them.
It is similar to a minimum points in transverse waves.

Wavelength, λ, is the distance between two adjacent crests of a wave.
It is the shortest distance between two points moving in phase.
Wavelength is measured in meters and can be found by finding the distance between two corresponding points on a wave.
Generally, it is easiest to look at maximum and minimum points, although any two points in phase would work.

For a longitudinal wave, the wavelength is the distance between consecutive rarefactions or consecutive compressions.

Period is the time taken for one complete wave to pass a point.
It is written as T and is measured in seconds.
Similar to simple harmonic motion, period is the distance between two points in phase in a displacement-time graph, where time is the x-axis.

Wavelength is measured in meters and is the distance between the end points on one cycle of wave.
Frequency is measured in the reciprocal of seconds, s⁻¹, and is the amount of cycles completed in a second.
The product of wavelength and frequency gives us ms⁻¹, and thus the wave speed.

Waves can be represented by displacement-position or displacement-time graphs.
They both have similar sinusoidal shapes, except displacement-position graphs can show wavelength, and displacement-time graphs show the period.

Both graphs can show the amplitude, which is the difference between the minimum or maximum point, and the x-axis, which is zero.

Sources

https://www.acs.psu.edu/drussell/demos/waves/wavemotion.html