Practice Questions Flashcards
general transverse wave
y(x,t) = Acos{kx±ωt+φ}
where φ is the offset
k =
2 pi / λ
positive propogation
to the left with a negative sign
i.e. kx - ωt
negative propogation
to the right with a positive sign
i.e. kx + ωt
the offset, φ, can be determined via
the boundary conditions
phase change is
ωt
dy/dt =
v
dv/dt =
a
displacement corresponds to which component
the REAL component
max values of displacement when
cos{kx±ωt} = 1
{kx±ωt} = 2 pi n
Show y(x,t) is a solution to the wave equation
- take the derivatives of y(x,t)
- substitute the derivatives into the wave equation
- solve to find a known relation
Energy density =
E/δx
δx =
∫ dx
progressive transverse wave
y(x,t) = y(x-ct)
where u = x-ct
dy/dt for a progressive transverse wave =
dy/du du/dt
dy/dx for a progressive transverse wave =
dy/du du/dx
units of impedance Z
kgs^-1
to convert from g to kg
x10^-3
linear density
rho, p
Transmitted energy coefficient T =
Et/Ei = C^2/A^2 Z2/Z1 = 4Z1Z2/(Z1+Z2)^2
mass derivation thingy
- Draw a Diagram
- Evaluate yi + yr = yt at boundary conditions (A+B=C)
- F = ma
- Fnet = T dy(t)/dx - T (dy(i)/dx + dy(r)/dx)
- substitute to F = ma
- evaluate derivatives at Boundary conditions
- multiply by -i
- C = A + B
- kT = Zω
for progressive waves to not be reflected
use impedance matching
impedance matching
Z2 = √(Z1Z3)
and
L = λ/4
Reflected Energy Coefficient R =
Er/Ei = B^2/A^2 Z1/Z1 = (Z1-Z3/Z1+Z3)^2