Please enable JavaScript.
Coggle requires JavaScript to display documents.
Mechanical Waves (New) (Types Of Mechanical Waves (Significance (The…
Mechanical Waves (New)
Types Of Mechanical Waves
Longitudinal
Particles move parallel to motion of the wave
Combination
The particles displacements have both longitudinal and transverse components
Traversal
Particles move perpendicular to motion of the wave
Significance
Disturbance propogates(travels) through medium with a definite speed
The medium itself doesnt travel
Water in waves in ocean don't move cross continents
Energy
Waves transport energy, but
not matter, from one region to another
General
Terms
Periodic Waves (SMH)
Equations/Relationships
Particles at same frequency
radians and unit circle
Mathematical Description of a Wave
Displacement of particle y(x,t)
Mathematical Derivation (If we know wavelength but not wave speed)
Snapshot of wave frozen in time
Consider time as shifting sin or cos
More intuitive interpretation (If we know wave speed but not wavelength)
y(x=0,t)
Displacement y of the particle at x=0 as a function of time
We use this as our graph and shift everything toward this interpretation
For example,
If x=30m and v=3m/s we can solve for how long it would take for the disturbance at x=0m to reach x=30m
\(speed=\frac{distance}{time}\) so t=30/3=10s
So if we wanted to find the displacement of x=3m at t=23s, remember that x=0m is 10s ahead. This means if we look at 13s we can see llok into the future and see what x=3m at t=23s would look like
This means that the particle at x=0 is 10 seconds ahead of x=3m
Phase velocity/speed
Running at same speed as a wave
Wave looks still
\(kx-wt=constant\)
Derivative respect to t
\(k\frac{dx}{dt}-w\frac{dt}{dt}\to k\frac{dx}{dt}-w=0\)
\(\frac{dx}{dt}=v=\frac{w}{k}\)
Wave equation
Speed of Tranverse Wave
Method 1: Assuming Shape (and constant v?)
Method 2: General
General Formula for Velocity
Energy
Power
\(W=F\Delta x\)
\(P=\frac{W}{\Delta t}\to \frac{F \Delta x}{\Delta t} \)
\(P=Fv\)
No net Force in x direction
\(P=F_y(x,t)v_y(x,t)\)
Intensity
Angular Frequency and Velocity
Angular refers to unit circle
Circle=(cos theta, sin theta)
Unit circle interpretation
Velocity
\(\omega\) = The degrees we cover per unit of time.
Similar to how velocity is distance over time
\(\theta\)=angular distance not degrees
Frequency
T=\(\frac{2\pi}{\omega}\)
The period T is the number of seconds it takes for 1 revolution if we travel one revolution \(2\pi\) going at a speed \(\omega\) we'd get the time it takes to cover one revolution
Inverting that we get how many revolutions are covered per second
Remember revolutions and radians are dimensionless
Think of it as how much of a circle we cover per unit of time
\(f=\frac{1}{T}=\frac{\omega}{w\pi}\)
Remember \(velocity=\frac{distance}{time}\) so \(time=\frac{distance}{velocity}\)
Sinusoidal graph interpretation
Velocity
How much angular distance we cover per unit of time
If we traveled one revolution in x seconds, it means we traveled \(\lambda\) meters in T seconds.
\(\omega=\frac{2\pi}{T}\)
Frequency
How many revolutions do we cover per unit of time?
How much of the wavelength do we cover per unit of time
Ex: If we cover half the wavelength in 10 seconds it means we covered .2 revolutions per second or .2 of the wavelength each second
