Wave Phenomena (topic 4 & 9) Flashcards
Equation for Simple Harmonic Motion
a = -w^2 x,
where
a = acceleration (ms^-2),
x = displacement from equilibrium (m),
w = angular frequency (rad * sec^-1)
Frequency of Oscilations equation
w = 2pi * f (frequency)(Hz) OR w = 2pi / T
SHM Displacement Equation
x = x0 sin (wt),
where
x = actual displacement (m),
x0 = max. displacement (m),
t = time (sec),
w = angular frequency (rad * sec^-1)
SHM Velocity Equation
v = w x0 cos(wt),
where
v = velocity,
w = angular frequency,
x0 = max. displacement,
t = time
OR
v = +-w squareroot x0^2 - x^2,
where
v = velocity,
w = angular frequency,
x0 = max. displacement,
x = actual displacement.
SHM Kinetic Energy Equation
Ek = 1/2 m w^2 (x0^2 - x^2),
where
Ek = kinetic energy,
m = mass,
w = angular frequency,
x0 = max. displacement,
x = actual displacement
SHM Total Energy Equation
ET = Ekmax = 1/2 m w^2 x0^2,
where
m = mass,
w = angular frequency,
x0 = max. displacement
Pendulum Equation
T = 2pi squareroot of l/g,
where
T =period (sec),
l = length of pendulum (m),
g = acceleration due to gravity on earth (ms^-2)
Spring Equation
T = 2pi squareroot of m/k,
where
T = period (sec),
m = mass (kg),
k = spring constant (Nm^-1)
Single Slit Diffraction Equation (first minimum)
theta = lambda / b,
where
theta = angle (radians),
lambda = wavelenth (m),
b = slit width (m).
***Use l = r * theta to find length,
where
l = lenth,
r = radius,
theta = angle
Multiple Slit Interference Equation
n * lambda = d sin theta,
where
n = order (n = 0,1,2,3,…),
lambda = wavelength (m),
d = slit separation (m)
Constructive Interference
path interference = n * lambda,
where
n = order (0,1,2,3,…),
lambda = wavelength (m)
Thin Film Interference (constructive)
2dn = (m + 1/2 lambda),
where
d = thin film thickness (m),
n = index of refraction,
m = order (0,1,2,3,…),
lambda = wavelength of light (m)
Thin Film Interference (destructive)
2dn = m lambda,
where
d = thin film thickness (m),
n = index of refraction,
m = order (0,1,2,3,…),
lambda = wavelelngth of light (m)
Thin Film Thickness Equation
d = 1/N,
where
d = thin film thickness,
N = diffraction grating
Resolution (Rayleigh Criterion)
Two objects are just resolved if theta = (1.22 * lambda) / b,
where
theta = angle between the two interferenc patterns (rad),
lambda = wavelength of light (m),
b = aperture width (m)
If:
theta is less than (1.22 * lambda)/b -> can’t tell them apart
theta is greater than or equal to (1.22 * lambda) / b -> can tell then apart
Resolution (Resolvance)
R = lambda / delta lambda = mN,
where
R = resolvance,
lambda = wavelength being investigated (m),
delta lambda = smallest possible resolvable wavelength difference (m),
m = diffraction order (0,1,2,3,…),
N = total number of slits being illuminated
Doppler Effect Moving Source Equation
f’ = f (v / v +-us),
where
f’ = observed frequency (Hz),
f = emitted frequency (Hz),
v = speed of sound (ms^-1),
us = speed of source (ms^-1)
smaller lambda = larger frequency
coming towards = higher pitch (frequency)
going away = lower pitch (frequency)
Astronomy Doppler Effect Equation
delta f / f = delta lambda / lambda approx. equal to v (speed) / c (speed of light)
Wave equation
v = fλ or c = fλ (for light)
where
v = speed (ms^-1)
f = frequency (Hz or sec^-1)
λ = wavelength (m)
c = speed of light (ms-1)
Frequency equation
f = 1 / T
where
f = frequency (Hz or sec^-1)
T = period (sec)
Transverse waves
Direction of oscillation is perpendicular to the direction of travel
Longitudinal waves
Direction of oscillation is parallel to the direction of travel
Intensity is proportional to the amplitude squared
I ∝ A^2
Intensity is inversely proportional to the square of the distance
I ∝ r^2
Reflection
θ1 = θ2
Critical angle
When the refracted angle is 90°
Total internal reflection
Any greater angle of 90° refraction (gets reflected)
Diffraction
When waves go through an aperture, they spread out
d > λ
When the slit width or aperture is bigger than the wavelength, not much diffraction
d ≤ λ
When the aperture is smaller or equal to the wavelength, more diffraction
Interference
When two waves meet, they can superpose with each other
Constructive interference
‘Add up’
Destructive interference
‘Cancel out’
Polarization
Plane of vibration of an electromagnetic wave (light)
Standing waves
Frequency and amplitude are constant, two waves meeting in superposition (in opposite directions)
Standing waves examples
- Fixed at both ends
- Open at one end, closed at the other
- Open at both ends
For small θ
sin θ = θ
