Vibrations and Waves Summary Sheet
Chapters 11 and 12
Anatomy and Ty pes of Waves
trough
crest
wavelength
amplitude
wavelength
extensions
compressions
Transverse Wave
Longitudinal Wave
Simple Harmonic Motion
m
m
m
m
m
Amplitude (A), max PE
Amplitude (A), max PE
Equilibrium (x = o), max KE
x = A sin(2πft)
or
x = A cos(2πft)
xmax = A
v = vmax(1-x2/A2)1/2
vmax = A (k/m)1/2
a = amaxcos(2πft)
amax = kA/m
T = 2π(m/k)1/2
f = 1/T
Etotal = ½ kx2 + ½ mv2
F = kx
m
m
m
T = 2π(l/g)1/2
Note: period not
dependent on mass
or amplitude
Notation
A = amplitude
f = frequency
T = period
x = displacement
v = speed
a = acceleration
t = time
m = mass
F = force on spring
k = spring constan t
l = pendulum length
g = 9.8m/s2
Wave Speed
v = λf general equation
l
m
F
v
ñ
E
v
T
=
=
v = wave speed
λ = wavelength
f = frequency
E = elastic modulus
ρ = density
FT = tension in string
l = length of string
m = mass of string
Using material
properties
(longitudinal)
Waves on a
string
(transverse)
Wave Properties
Reflection – upon encountering a new medium, a pulse or wave may “bounce” back
Transmission –upon encounteri ng a new medium, a portion of the wave continues into the new medium
Interference – occurs when mul tiple waves interact
Principle of superposition – to find the resulting wave, the disp lacements of each wave are added
Constructive – resulting amplitud e is greater than either Destructive – resulting amplitude is less than
pulse’s/wave’s amplitude either pulse’s/wave’s ampl itude
Refraction – wave changes direction due to a Diffraction – wave bends when it encounters
change in the medium through which it travels a barrier
Fixed end
Free end
θi
θr
Angle of incidence
equals angle of
reflection
Less dense to more de nse: amplitude decreases, wave slows
More dense to less dense: amplitude inc reases, wave spe eds up
Example:
Pulses on a
string
Example: water
waves hitting a
barrier
Example:
Pulses on string
