OWS

Question 1

What is the definition/formula for angular frequency?

Answer 1

ω, is defined by ω = 2 π f where f is defined as the number of oscillations per unit time.

Question 2

What is phase?

Answer 2

Phase is an angle in radians (rad) which gives a measure of the fraction of a cycle that has been completed by an oscillating particle or by a wave. {One cycle corresponds to 2π rad.}

Question 3

What is the formula for phase difference?

Answer 3

φ = x/λ x 2π = t/T x 2π

Question 4

What is simple harmonic motion? What is the formula?

Answer 4

Simple harmonic motion is an oscillatory motion in which the acceleration is always proportional to, and opposite in direction to the displacement from equilibrium position.
{MUST define where displacement is from}

Question 5

What is the formula for max velocity?

Answer 5

vo = xo ω

Question 6

What is the formula for max acceleration?

Answer 6

ao = xo ω2

Question 7

What is the formula for total energy?

Answer 7

Etotal = KE + PE at any instant = ½ mω2x02 = max KE = max PE

Question 8

What is the formula for total energy of vertical spring-mass system?

Answer 8

ET = EK + (GPE + EPE)

Question 9

What is the formula of period of vertical/horizontal spring-mass system?

Answer 9

T = 2π√m/k

Question 10

What is the formula for period of simple pendulum?

Answer 10

T = 2π√l/g

Question 11

What is damping? What is light/critical/heavy damping?

Answer 11

Damping refers to the loss of energy from an oscillating system to the environment, caused by a dissipative force acting in opposite direction of motion of the system, eg friction, viscous force.

Light Damping: The system oscillates about the equilibrium position with decreasing amplitude over a period of time.

Critical Damping: The system does not oscillate & damping is just adequate such that the system returns to its equilibrium position in the shortest possible time.
{Need to describe practical examples, eg, in analogue ammeters}

Heavy Damping: The damping is so great that the displaced object never oscillates but returns to its equilibrium position very very slowly.

{Need to illustrate these 3 degrees of damping with a displacement-time graph}

Question 12

What is free oscillation?

Answer 12

An oscillating system is said to be undergoing free oscillations if its oscillatory motion is not subjected to an external periodic driving force. Hence the system oscillates at its natural frequency.

Question 13

What is forced oscillation?

Answer 13

An oscillating system is said to undergo forced oscillations if it is subjected to an input of energy from an external periodic driving force. As a result, the frequency of the forced or driven oscillations will be at the frequency of the driving force [called the driving frequency] i.e. no longer at its own natural frequency.

Question 14

What is resonance?

Answer 14

a phenomenon whereby the amplitude of a system undergoing forced oscillations is at a maximum. ∙ It occurs when the frequency of the periodic driving force is equal to the natural frequency of the system.

Question 15

What are the 3 effects of damping on frequency response of a system undergoing forced oscillations?

Answer 15

1) resonant frequency decreases
2) sharpness of resonance [resonant peak] decreases
3) amplitude of forced oscillations decreases

Question 16

What is a progressive wave?

Answer 16

is the movement of a disturbance from a source which transfers energy from the source to places around it by means of vibrations/oscillations.

Question 17

What is a transverse/longitudinal wave?

Answer 17

Transverse wave: a wave in which the oscillations of the wave particles {NOT: movement/motion} are perpendicular to the direction of the propagation of the wave.
Longitudinal wave: a wave in which the oscillations of the wave particles are parallel to the direction of the propagation of the wave.

Question 18

What is wavelength of a wave?

Answer 18

λ: distance between 2 consecutive points on a wave which are in phase.

Question 19

What is the formula of wave speed of a wave?

Answer 19

v = ƒ λ {derived from v = λ / T and f = 1 / T}

Question 20

What is phase? What is phase difference?

Answer 20

is the angle which gives a measure of the fraction of a cycle that has been completed by an  oscillating particle or by a wave. {One cycle corresponds to 2π rad.} 
Phase difference (φ) is a measure of how much one wave is out of step with another wave or how  much one particle in a wave is out of step with another particle in the same wave. It is expressed  in terms of angles from 0 to 2π radians.

Question 21

What is intensity of wave? What is the formula of intensity of wave?

Answer 21

defined as the rate of energy flow [i.e. power] per unit cross-sectional area perpendicular to the direction of wave propagation
Intensity = Energy/Time x Area = Power/Area

Question 22

What is relationship between intensity and amplitude? Why?

Answer 22

For all types of wave sources, Intensity ∝ (Amplitude)2 since Total Energy ∝ A2

Question 23

What is the formula of intensity for a point source?

Answer 23

read notes

Question 24

What is the relation between intensity and distance from point source for constant power point source?

Answer 24

I ∝ 1/r2

since I ∝ A2 -> A ∝ 1/r

Question 25

What is polarisation?

Answer 25

Polarisation is a process by which the oscillations of the wave are confined to only one direction, in the plane normal to the direction of energy transfer.

A polarised wave is one whose oscillations are confined to only one direction, in the plane normal to the direction of energy transfer (propagation of the wave).

Only transverse waves can be polarized, longitudinal waves cannot.

Question 26

What is Malus’ Law?

Answer 26

I = Io cos2 θ ( Malus’ Law)
Intensity I of light transmitted by the analyzer is directly proportional to the square of the cosine of angle between the transmission axes of the analyzer and the polarizer.

Question 27

What is diffraction?

Answer 27

Diffraction refers to the spreading {not: bending} of waves when they pass through an opening [gap], or round an obstacle into the “shadow” region.
∙ For significant diffraction to occur, the size of the gap should be approximately equal to the wavelength of the wave.
∙ Diffraction of light provides evidence for the wave nature of light and all other electromagnetic radiation. Because the wavelength of light is very short (≅ 10-7 m), diffraction can only be observed through very narrow slits or small obstacles. Sound waves, however, are able to diffract around bigger objects because of their longer wavelength.

Question 28

What is principle of superposition?

Answer 28

When two or more waves of the same type meet/superpose {NOT: superimpose} at a point, the resultant displacement {NOT: amplitude} of the waves is equal to the vector sum of their individual displacements at that point.

Question 29

What is coherence?

Answer 29

Two waves are coherent if they have a constant phase difference (not just zero phase difference) between them (with respect to time).
∙ Common error: students wrongly think coherent waves must always be in phase with each other.

Question 30

What is interference? What is constructive/destructive interference?

Answer 30

Interference refers to the superposition of coherent waves which results in a change in the overall intensity.

Constructive interference:
This occurs when waves from two (or more) coherent sources arrive at a point in phase (i.e. zero phase difference), producing a resultant wave with amplitude that is the sum of the amplitudes of the individual waves.

Destructive interference:
This occurs when waves from two (or more) coherent sources arrive at a point in anti-phase (i.e. phase difference of π radians), producing a resultant wave of minimum amplitude and intensity.

Question 31

What are the conditions for constructive/destructive interference?

Answer 31

Using Path Difference:
For two sources in phase:
1. If constructive interference occurs at P,
the path difference (for the two ‘sources’ at S1 and S2) must be an integral multiple of the wavelength λ of the waves.
i.e. path difference = 0, 1 λ, 2 λ, 3 λ, … = n λ
{ with 2 antiphase sources 🡪 path difference = (n + ½) λ (odd multiples of half wavelengths) }
2. If destructive interference occurs at P,
the path difference will be an odd multiple of half wavelengths.
i.e. path difference = 0.5 λ, 1.5 λ, 2.5 λ, 3.5 λ, …
= (n + 1/2 ) λ or (2n + 1)/2 λ
{ with 2 antiphase sources 🡪 path difference = n λ }
In both cases, n = 0, 1, 2, 3, …
Using Phase Difference:
3. If constructive interference occurs at P,
phase difference of the 2 waves meeting at P = (n) 2π radians { 0, 2π, 4π, etc }
4. If destructive interference occurs at P,
phase difference of the 2 waves meeting at P = (n + ½) 2π radians { π, 3π, 5π etc } In both cases, n = 0, 1, 2, 3, …

Question 32

What are the conditions for well-defined interference patterns?

Answer 32

(i) coherent,
(ii) have about the same amplitude (equal is best),
(iii) meet / superpose
(iv) be polarised in the same direction, or unpolarised (only for transverse waves)

Question 33

What is the formula for Young’s double slit expt.?

Answer 33

fringe separation, x =λD/a applicable only if a &laquo_space;D & λ &laquo_space;a

where x: distance between 2 successive bright fringes (or 2 dark fringes).
λ: Wavelength of light.
D: distance between the double slits and the screen.
a: distance between the 2 double slits.

Question 34

What is the resultant intensity of 2 waves with different intensities at a pt. of CI and DI?

Answer 34

x

Question 35

What is the formula for single-slit diffraction?

Answer 35

Angular position of First Minima: sin θ = λ/b where b = slit width.
when θ is small, then θ = bλ {in radians}
the central maximum is twice as wide (2λ/b wide) as any of the other secondary maxima (λ/b wide each).

Question 36

What is rayleigh criterion? What is the formula for limiting angle of resolution?

Answer 36

Rayleigh criterion states that 2 images are said to be just resolved if the central maximum of one image falls on the first minimum in the diffraction pattern of the other.
θmin ≈ λ/b

Question 37

When are the images just/obviously/not resolved?

Answer 37

∙ If the actual angle subtended by the two point sources at the slit, θs = θmin, then the images are just resolved (by Rayleigh’s criterion).
∙ θs must be > θmin if the images are to be obviously resolved.
∙ Conversely, if θs < θmin , the images are not resolved.

Question 38

What is the formula of diffraction grating? What is the maximum number of orders/bright fringes?

Answer 38

maxima are located at angular positions defined by θ in : d sin θ = n λ
where: d: slit separation (grating or line spacing ) is the distance between adjacent slits θ : angle of diffraction /angular deviation /angle of deviation (measured from the normal)
n: order of diffraction (must be an integer or zero)
λ: wavelength
The maximum number of orders can be found by substituting θ = 90°
nmax = d / λ (rounded down to nearest integer)
Hence maximum number of bright fringes (displayed on screen) = 2nmax + 1

Question 39

What are stationary waves? How was it formed?

Answer 39

Stationary (standing) wave is one
∙ whose waveform/wave profile does not advance /move,
∙ where there is no net transport of energy, and
∙ where the positions of antinodes and nodes do not change, or where there are certain points which are permanently at rest. {last bullet is least impt}
A stationary wave is formed when two progressive waves of the same frequency, amplitude and speed, travelling in opposite directions are superposed.

Question 40

What are the differences between stationary waves and progressive waves?

Answer 40

look at notes

Question 41

What is a node/anti-node? What is the distance between 2 successive nodes/anti-nodes?

Answer 41

∙ Node: a region of destructive superposition where the waves always meet out of phase by π radians. Hence displacement here is permanently zero {or minimum}

∙ Antinode: a region of constructive superposition where the waves always meet in phase. Hence a particle here vibrates with maximum amplitude.
{but it is NOT a point with a permanent large displacement! J08P2Q5b, 1m}

∙ Distance between 2 successive nodes/antinodes = λ/2