Topic 9: Wave phenomena (HL) Flashcards
[DATA BOOKLET]
Equation for [???] in SHM
(??) = -ω2x0cos(ωt)
acceleration
(a)
[DATA BOOKLET]
Equation for [???] in SHM
(??) = -ω2x0
MAXIMUM acceleration
(amax)
[DATA BOOKLET]
Equation for [???] in SHM
(??) = -ωx0 sin(ωt);
(??) = ωx0 cos(ωt)
velocity
(v)
[DATA BOOKLET]
Equation for [???] in SHM
(??) = -ωx0
MAXIMUM velocity
(Vmax)
[DATA BOOKLET] Equation for [???] in SHM = x0 sin(ωt); = x0 cos(ωt)
displacement (x)
How do you know whether to use -sin(ωt) or cos(ωt) for velocity in SHM?
for SHM the derivation depends on the original displacement graph/function. [if displacement was sin(ωt) then velocity will be cos(ωt); if displacement was cos(ωt) then velocity will be -sin(ωt)]
How does the total energy of a system change during SHM?
it stays constant (total energy = kinetic energy + potential energy)
What is the shape of a displacement graph for simple harmonic motion (SHM)?
Sinusoidal
Write SHM as an equation
a = -(ω2)x
What is acceleration proportional to in SHM?
negative displacement (a ∝ -x)
What is the restoring force in a simple pendulum?
m⋅g⋅sinθ
What is x0?
maximum displacement (amplitude)
When in kinetic energy maximum in SHM?
displacement = 0; x = 0
When in kinetic energy minimum in SHM?
at maximum displacement (amplitude)
x = x0
When in potential energy maximum in SHM?
displacement = x0; at maximum displacement (amplitude)
When in potential energy minimum in SHM?
displacement = 0
x = 0
In what direction does the acceleration in SHM act?
Towards the equilibrium point
(x=0)
What is ω and its unit?
angular frequency
rad s-1
How do you identify if SHM is taking place?
- Identify forces when object is displaced from rest position (free-body diagram)
- Calculate resultant force using Newton’s second law: if the force is proportional to displacement and the direction is always towards rest position, then there is SHM.
- ω2 = (restoring force per unit displacement/mass)
Assumptions for SHM (vertical spring)
- mass of spring is negligible (compared to the mass of load)
- friction (air friction) is negligible
- spring obeys Hooke’s law at all times (elastic limit is not exceeded)
- gravitational field strength, g, is constant
- the spring’s fixed end cannot move
Assumptions for SHM (simple pendulum)
- mass of the pendulum is negligible compared to that of the load
- friction (air friction) is negligible
- the maximum angle of swing is small (≤ 5
[DATA BOOKLET]
What does each symbol mean and what is its unit?
ω = 2π/T
ω is angular frequency, in rad s-1
T is time period, in s
Equation for velocity in SHM (no trig functions)
v = ±ω√( x02 - x2 )
If displacement follows a positive sin function, what functions will velocity and acceleration follow?
x = sin ωt
v = cos ωt
a = -sinωt
[NOTE: these are not the full equations, just the trig function part]
If displacement follows a negative sin function, what functions will velocity and acceleration follow?
x = -sin ωt
v = -cos ωt
a = sin ωt
[NOTE: these are not the full equations, just the trig function part]
If displacement follows a positive cos function, what functions will velocity and acceleration follow?
x = cos ωt
v = -sin ωt
a = -cos ωt
[NOTE: these are not the full equations, just the trig function part]
If displacement follows a negative cos function, what functions will velocity and acceleration follow?
x = -cos ωt
v = sin ωt
a = cos ωt
[NOTE: these are not the full equations, just the trig function part]
What was Huygen’s principal?
treat a wavefront as a number of wave sources
When does maximum diffraction occur?
when the gap is the same width as the wavelength of the wave passing through it
What is the single slit equation?
θ = (nλ)/b
- θ is the angle between the middle of the slit to the fringe (minimum)
- n is the fringe (minimum) number
- λ is the wavelength
- b is the slit width
What is diffraction?
the bending of waves around a barrier or through an opening.
How does increasing wavelength affect the angle of diffraction?
Increasing wavelength increases the angle of diffraction
θ = (nλ)/b