Wave Phenomena (topic 4 & 9)

Question 1

Equation for Simple Harmonic Motion

Answer 1

a = -w^2 x,

where
a = acceleration (ms^-2),
x = displacement from equilibrium (m),
w = angular frequency (rad * sec^-1)

Question 1

Frequency of Oscilations equation

Answer 1

w = 2pi * f (frequency)(Hz) OR w = 2pi / T

Question 2

SHM Displacement Equation

Answer 2

x = x0 sin (wt),

where
x = actual displacement (m),
x0 = max. displacement (m),
t = time (sec),
w = angular frequency (rad * sec^-1)

Question 3

SHM Velocity Equation

Answer 3

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.

Question 4

SHM Kinetic Energy Equation

Answer 4

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

Question 5

SHM Total Energy Equation

Answer 5

ET = Ekmax = 1/2 m w^2 x0^2,

where
m = mass,
w = angular frequency,
x0 = max. displacement

Question 6

Pendulum Equation

Answer 6

T = 2pi squareroot of l/g,

where
T =period (sec),
l = length of pendulum (m),
g = acceleration due to gravity on earth (ms^-2)

Question 7

Spring Equation

Answer 7

T = 2pi squareroot of m/k,

where
T = period (sec),
m = mass (kg),
k = spring constant (Nm^-1)

Question 8

Single Slit Diffraction Equation (first minimum)

Answer 8

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

Question 9

Multiple Slit Interference Equation

Answer 9

n * lambda = d sin theta,

where
n = order (n = 0,1,2,3,…),
lambda = wavelength (m),
d = slit separation (m)

Question 10

Constructive Interference

Answer 10

path interference = n * lambda,

where
n = order (0,1,2,3,…),
lambda = wavelength (m)

Question 11

Thin Film Interference (constructive)

Answer 11

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)

Question 12

Thin Film Interference (destructive)

Answer 12

2dn = m lambda,

where
d = thin film thickness (m),
n = index of refraction,
m = order (0,1,2,3,…),
lambda = wavelelngth of light (m)

Question 13

Thin Film Thickness Equation

Answer 13

d = 1/N,

where
d = thin film thickness,
N = diffraction grating

Question 14

Resolution (Rayleigh Criterion)

Answer 14

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

Question 15

Resolution (Resolvance)

Answer 15

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

Question 16

Doppler Effect Moving Source Equation

Answer 16

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)

Question 17

Astronomy Doppler Effect Equation

Answer 17

delta f / f = delta lambda / lambda approx. equal to v (speed) / c (speed of light)

Question 18

Wave equation

Answer 18

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)

Question 19

Frequency equation

Answer 19

f = 1 / T

where
f = frequency (Hz or sec^-1)
T = period (sec)

Question 20

Transverse waves

Answer 20

Direction of oscillation is perpendicular to the direction of travel

Question 21

Longitudinal waves

Answer 21

Direction of oscillation is parallel to the direction of travel

Question 22

Intensity is proportional to the amplitude squared

Answer 22

I ∝ A^2

Question 23

Intensity is inversely proportional to the square of the distance

Answer 23

I ∝ r^2

Question 24

Reflection

Answer 24

θ1 = θ2

Question 25

Critical angle

Answer 25

When the refracted angle is 90°

Question 26

Total internal reflection

Answer 26

Any greater angle of 90° refraction (gets reflected)

Question 27

Diffraction

Answer 27

When waves go through an aperture, they spread out

Question 28

d > λ

Answer 28

When the slit width or aperture is bigger than the wavelength, not much diffraction

Question 29

d ≤ λ

Answer 29

When the aperture is smaller or equal to the wavelength, more diffraction

Question 30

Interference

Answer 30

When two waves meet, they can superpose with each other

Question 31

Constructive interference

Answer 31

‘Add up’

Question 32

Destructive interference

Answer 32

‘Cancel out’

Question 33

Polarization

Answer 33

Plane of vibration of an electromagnetic wave (light)

Question 34

Standing waves

Answer 34

Frequency and amplitude are constant, two waves meeting in superposition (in opposite directions)

Question 35

Standing waves examples

Answer 35

1. Fixed at both ends
2. Open at one end, closed at the other
3. Open at both ends

Question 36

For small θ

Answer 36

sin θ = θ