Equations

Question 1

For a Sinusoidal travelling wave the displacement is ?

Answer 1

y(x,t) =Asin(kx±⍵t+ϕ)

Question 2

For a sinusoidal travelling wave what does (kx-⍵t) mean? What does that infer a + would mean?

Answer 2

That the wave is travelling to the right. infers that + means the wave is travelling left (negative x-direction)

Question 3

Wavenumber, K = ?

Answer 3

2π/wavelength

Question 4

What would a wave function that represents Displacement in space at fixed time look like?

Answer 4

y(x)=Asin(kx+ϕ)

Question 5

What would a wave function that represents Displacement in time at fixed x look like?

Answer 5

y(t)=Asin(-⍵t+π/2)

Question 6

angular frequency, ⍵ =?

Answer 6

2π frequency =2π/period

Question 7

Wave speed, v =?

Answer 7

angular frequency /wavenumber = frequency λ

Question 8

For Waves on a string , wave speed =?

Answer 8

= \sqrt {String tension}/{mass of string/length of string}

Question 9

Doppler Effect for sound

Answer 9

f ‘ = f (v±vdetector)/(v±vsource)

Question 10

Wave Equation

Answer 10

δ²y(x,t)/δt² = v² δ²y(x,t)/δx²

Question 11

The soultion to the wave equation is any function with the form

Answer 11

y(x,t) = f(x±vt)

Question 12

wavelength = ?

Answer 12

2π/k

Question 13

period = ?

Answer 13

2π/⍵

Question 14

frequency = ?

Answer 14

⍵/2π = 1/T

Question 15

velocity = ?

Answer 15

⍵/k = λ/T = fλ

Question 16

ϕ means ?

Answer 16

Phase change

Question 17

Superposition

Answer 17

y(x,t) = y1(x,t) + y2(x,t) …..

Question 18

Standing waves

Answer 18

2Asin(kx)cos(⍵t)

Question 19

Standing waves on a string length = ?

Answer 19

nλ/2

Question 20

Beat frequency , f beat = ?

Answer 20

f1-f2

Question 21

Beat waves = ?

Answer 21

2AoCos(⍵’t)sin(⍵t)

Question 22

what angular frequencies do beat waves oscillate with

Answer 22

Average angular frequency and Half angular frequency difference.

Question 23

Average angular frequency for beat waves = ?

Answer 23

1/2 (⍵1+⍵2)

Question 24

Half angular frequency difference for beat waves = ?

Answer 24

⍵’ = 1/2 (⍵1-⍵2)

Question 25

Superposition with a phase difference = ??

Answer 25

2Asin(kx-⍵t+ϕ/2)cos(ϕ/2)

Question 26

What is the trigonometric identity use din superposition with a phase difference

Answer 26

Sum of two sines is twice the sine of half the sum time cosine of half the difference. sin(x)+sin(y)=2sin(x+y/2)cos(x-y/2)

Question 27

Give me values on the visible light electromagnetic spectrum

Answer 27

a wavelength of 400nm for violet a wavelength of 700nm for red a wavelength of 560nm for the solar peak.

Question 28

Intensity = ?

Answer 28

<(Asin(kx-ωt))^2> Bracket indicate average over time

Question 29

What is intensity proportional to?

Answer 29

Amplitude squared

Question 30

snell's Law

Answer 30

n1sinθ1=n2sinθ2

Question 31

Refraction principle

Answer 31

when light travels from an optically less dense (smaller n) into an optically more dense medium (larger n) it bends towards the normal

Question 32

Critical angle = ?

Answer 32

arcsin(n2/n1)

Question 33

Wave speed (v) inside a material of refractive index n =?

Answer 33

c/n

Question 34

Phase velocity equation

Answer 34

Vp = ⍵/k

Question 35

what part of the wave moves at the phase velocity ?

Answer 35

The peaks

Question 36

Group velocity equation

Answer 36

Differentiate dispersion relation δ⍵(k)/δk Dispersion relation = ⍵(k) wave-packet moves at these velocities

Question 37

non-dispersive waves have a dispersion relation of = ?

Answer 37

⍵(k) = kVp

Question 38

For non-dispersive waves what is the relation between the group and phase velocity?

Answer 38

They are identical

Question 39

what changes in a wave undergoing reflection/refraction ?

Answer 39

The frequency doesn't change It's wavenumber/length and speed do.

Question 40

optical path length, L = ?

Answer 40

nd where; d is the physical path length

Question 41

light travel time, t = ?

Answer 41

L/c where ; L is the optical path length

Question 42

State Fermat's principle

Answer 42

The paths taken by light rays between two points are those that minimize the total time for travel. Light rays take the minimum (local minimum within constraints of problem) optical path length between to points.

Question 43

Light reflecting off of a medium of higher refractive index has a phase shift of ??

Answer 43

π

Question 44

light reflecting off of a medium of lower refractive index has a phase shift of?

Answer 44

Zero

Question 45

law of reflection

Answer 45

θ incident = θ reflection

Question 46

Law of refraction

Answer 46

n1sinθ1=n2sinθ2

Question 47

A negative power always indicates what?

Answer 47

A diverging lens

Question 48

Thin Lens Lens-makers formula

Answer 48

1/f = (n-1)(1/R1 - 1/R2)

Question 49

A positive power always indicates what?

Answer 49

A converging lens

Question 50

Magnification

Answer 50

h1/h0 = (-v)/u

Question 51

Gaussian Thin Lens Equation

Answer 51

1/u + 1/v = 1/f

Question 52

How to tell if an image is real ?

Answer 52

1. Focal length greater than zero 2. Object distance greater than focal length 3,. Magnification is negative so image in inverted

Question 53

Rules for drawing Lens diagrams

Answer 53

1. Rays through the lens centre do not change direction 2. Rays that enter in parallel converge at the focal point 3. Rays that diverge from the focal point end up parallel

Question 54

Total Magnification for Two lenses =

Answer 54

Mt = M1M2

Question 55

Two lenses in contact focal length =

Answer 55

1/Fe = 1/f1 + 1/f2

Question 56

lens power, p = ?

Answer 56

1/f

Question 57

Effective power of two lenses in contact = ?

Answer 57

Pe= P1+P2 Adds in series

Question 58

Overall focal length of two well separated lenses

Answer 58

1/F = 1/f1 - 1/(d-f2)

Question 59

Magnification of a galilean telescope

Answer 59

M = θ eyepiece/θ object = f1/f2

Question 60

Interference Intensity

Answer 60

2A²cos²(1/2k(D1-D2))

Question 61

Interference Bright Fringes Found

Answer 61

mλ=dsinθ

Question 62

Interference Dark fringes found

Answer 62

(m+1/2)λ=dsinθ

Question 63

Bragg's Law for X-ray Crystallography

Answer 63

mλ=2dsinθ

Question 64

Kinetic Energy of a phtoelectron

Answer 64

Ek=eVs

Question 65

Energy of a photon

Answer 65

E=hf h -> Planck's Constant

Question 66

What is the value of Planck's Constant

Answer 66

6.626x10^{-34}

Question 67

reduced planck constant

Answer 67

h/2π