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Physics > Chapter 8-10. Oscillations - Superposition > Flashcards

Chapter 8-10. Oscillations - Superposition Flashcards

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1
Q

Define Simple Harmonic Motion and give examples

A

A simple harmonic motion is an oscillatory motion whose acceleration is
1. directly proportional to the displacement from its equilibrium point
2. and is always in opposite direction to the displacement
a = -ω^2x

Eg. Simple pendulum

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2
Q

Define Periodic Motion and give examples

A

Periodic motion refers to any motion that repeats itself at equal intervals of time

Eg. Vibration of a tuning fork

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3
Q 
Formulae for SHM
1. Displacement
2. Velocity x 3 
3. Acceleration x 2
and 
4. v0
5. a0
A
  1. x = x0sinωt
  2. v = (w)x0sinωt
    v = (+-)ωsqrt(x0^2 - x^2)
    v = v0sinωt
  3. a = (w^2)x0sinωt
    a= a0sinωt
  4. v0 = wx0
  5. a0 = (w^2)x0
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4
Q

Formulae for Energy in SHM

  1. KE
  2. PE
  3. TE
A

lazy type. KE and TE can be derived

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5
Q

Define Resonance

A

Resonance is a phenomenon in which an oscillatory system responds with maximum amplitude to an external periodic driving force, when the frequency of the driving force (driver frequency) equals the natural frequency of the driver system

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6
Q

Define

  1. Forced oscillation
  2. Driving force
  3. Forced Frequency/ Driver frequency
A
  1. An oscillation under the influence of an external periodic force
  2. The external force that is used to drive the oscillations
  3. The frequency with which the periodic force is applied is called the driver frequency
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7
Q

Recall free oscillations, the types of damping and characteristics of their graphs as damping becomes greater

A
  1. Free oscillations is when a system oscillates about the equilibrium position with no other external forces. Therefore it is in its natural frequency
  2. Light damping. Amplitude decreases exponentially with time
  3. Critical damping. Returns to the equilibrium position in the shortest time possible without oscillating at all
  4. Heavy damping. Takes a long time to return to its equilibrium position. Overdamped

As the system experiences greater damping,

  1. Amplitude decreases
  2. Resonance peak becomes broader
  3. Resonance peak shifts slightly to the left to a slightly lower value of frequency
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8
Q

Define :

  1. Wave
  2. Transverse Wave
  3. Longitudinal Wave
  4. Progressive Waves
A
  1. A wave is disturbance that is able to transmit energy or momentum from a source to its surroundings. However, points in the system that carry the wave do not actually move from the source through the region the waves move through
  2. A transverse wave is a wave in which the points of disturbance oscillate about their equilibrium positions perpendicular to the direction of wave travel
  3. A longitudinal wave is a wave in which the points of disturbance oscillate about their equilibrium position in a direction parallel to the direction of wave travel
  4. Progressive waves are in which the wave profile moves away from the source and causes energy to be transferred away from the source to other regions
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9
Q

What equation relates phase, displacement and time?

A

∆t/T = ∆Ø/2π = ∆x/λ

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10
Q

Relationship between energy and amplitude, intensity and amplitude, intensity and radius

A
  1. Energy and intensity is proportional to square of amplitude
  2. For spheres, intensity = power/area = P/4πr^2
  3. Intensity is therefore inversely proportional to radius

Intensity - Wm-2
Power - Js-1 or W

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11
Q

What are the sources and uses of various waves?

A

lazy type

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12
Q

How to calculate intensity of light after being polarised?

A

I = I0 (cosθ)^2

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13
Q

Define Polarisation

A

Polarisation is a phenomenon whereby vibrations in a transverse wave are restricted to only one direction, in the plane normal to the direction of energy transfer

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14
Q

Define the Principle of Superposition

A

The principle of superposition states that when two or more waves of the same kind overlap, the resultant displacement at any point at any instant is given by the sum of the individual displacements that each individual wave would cause at that point at that instant

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15
Q

Define Interference

A

Interference is the superposing or overlapping of two or more waves to give a resultant wave whose displacement is given by the Principle of Superposition, which states that displacement of the resultant wave at any point is the vector sum of the displacements of the individual waves at that point

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16
Q

Define and Compare the differences between constructive and destructive interference. 2 things to compare.

A
  1. Constructive interference occurs at a point when two waves meet in phase at that point. The resultant amplitude of the oscillation at that point is therefore a maximum
    - Phase difference between the 2 waves at that point = 0, 2π, 4π, … = 2mπ
    - Path difference δ = |S1P - S2P| = mλ
  2. Destructive interference occurs at a point where two waves meet in antiphase. The resultant amplitude of the oscillation at that point is therefore a minimum.
    - Phase difference = π, 3π, 5π, … = (m-0.5)2π
    - Path difference = |S1P - S2P| = (m - 0.5)λ

where m is a positive integer

17
Q

Define diffraction

A

Diffraction is the spreading of waves, after passing through small apertures or openings, into their “geometrical” shadows; or the spreading of waves round an obstacle

18
Q

Define coherence and list the conditions for coherence

A

Two waves are said to be coherent if they have a constant phase difference between them.
Does not necessarily mean that they are in phase.

Same frequency and wavelength ( therefore same speed)

19
Q

List the conditions for interference to occur at a point

A
  1. Waves must be of the same kind

2. The waves must overlap, i.e. the waves must be at the same place at the same time

20
Q

List the conditions for permanent and observable interference pattern

A
  1. The sources must be coherent
  2. The 2 wave sources must emit waves of roughly the same amplitude
  3. For transverse wave, they must either be unpolarised or share a common direction of polarisation
21
Q

State the similarities and differences between Young’s double slit pattern and the diffraction grating

A

Similarity :
1. For the same slit separation d, the positions of maxima remain the same

Difference :
1. As the number of slits increase, the maxima become narrower

  1. As the number of slits increases, the intensity of the maxima increases
22
Q

Advantages and Disadvantages of using the higher order maximas to determine wavelength as compared to first order

A

Advantage : Angular displacement is larger so less percentage uncertainty in measuring the angle

Disadvantage : May not be as bright as the first order bright fringe

23
Q

Define stationary waves and state 2 characteristics

A

When 2 identical waves of the same amplitude, frequency and speed but travelling in opposite directions are superimposed together, the resultant wave obtained is called a stationary wave.

  1. Wavelength is 2*distance between a pair of adjacent nodes
  2. Waveform does not advance
    got more but lazy type
24
Q

What are 2 ends of the strings which are fixed in placed called? What is the middle called?

A

2 ends are displacement nodes. Middle is displacement antinode since greatest displacement

25
Q
  1. Formulae for open pipe and closed pipe (total 4)
    and
  2. Location of displacement nodes and antinodes
A

Open Pipe :
1. f = n(v/2L)
where n = 1, 2, 3, 4, …
2. L = n(λ/2)

Closed Pipe :
1. f = n(v/4L)
where n = 1, 3, 5, …
2. L = n(λ/4)

Closed end is displacement node, open end is displacement antinode

26
Q

List all formulae for diffraction grating

A 
d - slit separation
y - positions of light and dark fringes
∆y - Fringe separation
L - distance of slit from viewing screen
N - no. of lines per unit length
m & n are both order numbers = 0, 1, 2, 3, ...

Young’s double slit :
1. Constructive Interference : dsinθ = mλ
2. Destructive Interference : dsinθ = (m-0.5)λ
Assume L is much larger than d

  1. tanθ = y/L (Assume λ is much smaller than d)
  2. y = m(λL)/d
  3. ∆y = λL/d
    Assume 1. θ is small
    2. L is Larger than d
  4. and 5. cannot be used for diffraction grating unless fringes are regularly spaced

Difrreaction Grating :

  1. Constructive Interference : dsinθ = nλ
  2. N = 1/d
27
Q

For the formula dsinθ = nλ, how to find n with θ unknown?

And how to find θ?

A
  1. sinθ = nλ/d
  2. nλ/d smaller than or equal to 1
  3. solve for n - obtain n smaller or equal to decimal
  4. Round down to nearest integer
  5. Sub value of n, λ and d to find θ
28
Q

Number and location of nodes and antinodes in open and closed pipe

A

Open Pipe : 1 more antinode than node
Closed Pipe : Same number of nodes and antinodes

Closed pipe has no node or antinode in the centre.

29
Q

Define node and antinode

A

Node is a region in a stationary wave where amplitude of oscillation is zero

Antinode is a region in a stationary wave where amplitude of oscillation is a maximum

Physics (6 decks)

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