Experimental Data Flashcards

1
Q

Notations like mega pico etc

A

learn off

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2
Q

Types of data

A

Quantitative

Qualitative

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3
Q

Quantitative data

A

eg.
length = 1.24m
24 types of paints used
fram is manufactured o alpha brass

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4
Q

Qualitative data

A

eg.
it is a sad painting
masterful brush strokes

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5
Q
SI unit of:
mass
length
time
electrical current
temperature 
luminous intensity
amount of substance
A
kg
m
s
A
K
cd
mol
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6
Q

femto f

A

x 10 ^ -15

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7
Q

pico p

A

x 10 ^ -12

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8
Q

nano n

A

x 10 ^ -9

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9
Q

micro μ

A

x 10 ^ -6

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10
Q

milli m

A

x 10 ^ -3

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11
Q

centi c

A

x 10 ^ -2

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12
Q

kilo k

A

x 10 ^ 3

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13
Q

mega M

A

x 10 ^ 6

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14
Q

giga G

A

x 10 ^ 9

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15
Q

tera T

A

x 10 ^ 12

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16
Q

tabulating data

A

book pg 13

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17
Q

sensors

A

detect energy

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18
Q

transdurcers

A

convert energy from one form to another

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19
Q

is a microphone a sensor or a transducer?

A

-detects and converts sound energy to electrical energy - it is both

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20
Q

is a loudspeaker a sensor or a transducer?

A

-converts electrical energy to sound energy - a transducer

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21
Q

sensors and energy

A

no sensor is sensitive to only one form of energy

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22
Q

Measurement instrument

A

a measurement system

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23
Q

scientific instruments

A
  • high quality measurement systems

- due to high accuracy + low uncertainty

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24
Q

how measurement systems work

A
  • transducer/sensor provides input to instrument

- instrument manipulates (amplify, filter, convert to digital representation) input signal to provide useful output

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25
Q

The correct device has:

A

req accuracy
stability
robustness
appropriate cost

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26
Q

types of quantities

A

static

dynamic

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27
Q

static quantities

A

slowly varying quantities

eg. a building height

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28
Q

dynamic quantitites

A

rapidly varying quantities

eg. sound, temperature

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29
Q

performance characteristics of instruments

A
  • range
  • span
  • linearity
  • non-linearity
  • hysteresis
  • resolution
  • repeatability
  • accuracy
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30
Q

range

A

min and max values of input or output variables

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31
Q

span

A

maximum variation of input or output variables

eg. thermometer with range -40C to 100C, span is 140C

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32
Q

linearity

A

extent to which input values and output values lie on (or near) a straight line

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33
Q

non-linearity

A

a more complex relationship between input and output

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34
Q

hysteresis

A

some instruments have different loading and unloading performance

(some sensors behave differently during loading and unloading, eg. due to friction between components in instrument)

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35
Q

resolution

A

smallest change in a variable to which the instrument will respond.

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36
Q

repeatability

A

measure of the closeness of agreement between a number of readings taken consecutively of a variable, before the variable has time to change.

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37
Q

accuracy

A

difference between the indicated value and the actual value.

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38
Q

If instrument preforms with ideal linear behaviour then relationship between input and output can be expressed as:

A

y = Ax

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39
Q

Drift

A

eg. a change to ambient temp may cause a drift in output of instrument which is not due to a change in measured variable

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40
Q

Impact of drift

A
  • zero drift

- sensitivity drift

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41
Q

calibration

A

process of validating a measurement technique or instrument

-compare performance of instrument w/ known standard

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42
Q

static calibration

A
  • to obtain static characteristics of an instrument
  • establish relationship between input (measurand) + output
  • hold all inputs steady
  • vary measurand + record output
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43
Q

standards

A

primary

secondary

44
Q

primary standards

A

standards are complex and expensive, usually held by government agencies. Such as the National Institute of Standards and Technology in the US.

45
Q

secondary standards

A

less expensive and less accurate.

eg. from National Laboratories, Universities

46
Q

Tertiary Standard

A

In house calibration

47
Q

Sig figures rules

A
  • count all figures eg. 6.12 has 3 sig figs
  • for decimals with lots of zeroes, counta ll digits to right of 1st non-zero eg. 0.001246 has 4 sig figs

check notes

48
Q

multiplying or dividing sig figs

A
  • result should have same number of sig figs as number with least sig figs
    eg. 3.7 x 3.01 = 11.137 = 11
49
Q

adding or substracting sig figs

A

numbers round the result to the same number of significant digits as that number with the least number of significant digits

eg. 11.24 + 13.1 = 24.34 = 24.3

50
Q

Types of rounding

A

Truncation
Round to nearest even
Ceiling
Flooring

51
Q

Sig figs - what does 6.124 mean?

A

number is between 6.123 and 6.125

52
Q

uncertainties: writing them

A

eg.

(15. 5 +- 0.5)°C

53
Q

truncation

A

round towards zero, discard least sig figures

eg: truncated to 4 sig figures:

  1. 672 = 45.67
  2. 45812 = 45.45
54
Q

Round to nearest even

A

If LSD > 5 increment next LSD

If LSD < 5 truncate LSDs

tie breaking rule for when x is half way between 2 integers

check otes

55
Q

how to decide how many sig figs

A

depends on precision and accuracy

56
Q

accuracy

A

describes how well a measurement agrees with a known standard.

accurate if readings close to ‘true’ value

57
Q

precision

A

describes the degree of certainty about the measurement.

precise if readings closely grouped

58
Q

measured value and its uncertainty

A

must always have same no. of digits after decimal place

eg
g=(9.802 +- 0.0001)[m/s2]

59
Q

Resolution uncertainty

A

check slides 3

60
Q

use of mean

A

often used to smooth out the variation

best estimate, but still uncertain

61
Q

we can’t know the TRUE value

A

but reasonable to assume that true value lies within range of extremes (in between max and min values)

62
Q

mean (𝑥̅) formula

A

check slides 3

63
Q

calculating uncertainty in the mean

A
  1. calculate range (largest - smallest value)
  2. divide range by number of measurements
    - only quote one sig figure eg. 0.0825 = 0.08
    - quote mean to same number of decimal places as uncertainty
64
Q

random errors

A
  • measurements subject to random errors, cause measurement to fluctuate above and below true value
  • best approach is to take repeated measurements
  • determine uncertainty from spread
  • mean is best estimate of true value
65
Q

deviation of one measurement from mean formula

A

𝑑ᵢ =𝑥ᵢ − 𝑥̅

66
Q

Spread - Variance formula

A

in lecture slides 4

units of variance are square of those of the measurand

67
Q

standard deviation

A

measure of how much indiv measurements are likely to vary from mean value

68
Q

reduce uncertainty

A

more measurements (increasing n)

69
Q

standard deviation of the means

A

standard error in the mean

-know how to use formula

70
Q

relationship between standard error in mean and standard deviation formula

A

σ𝑥̅ =σ/√𝑛

71
Q

Adding measurements with uncertainty

A

-Uncertainty in computed measurement is the SUM of the uncertainties in the individual measurements

(X +- △X) + (Y +- △Y) = (X + Y) +- (△X + △Y)

72
Q

subtracting measurements with unceratainties

A

Uncertainty in computed measurement is the SUM of the uncertainties in the individual measurements.

(X +- △X) - (Y +- △Y) = (X - Y) +- (△X + △Y)

uncertainties not subtracted

73
Q

multiplying two measurements with uncertainties

A

(X +- △X)(Y +- △Y)

do algebraically, and get

XY(1 +- △X/X +- △Y/Y)

74
Q

Fractional uncertainty in X

Fractional Uncertainty in Y

A

△X/X

△Y/Y

75
Q

what x y △x and △y stand for

A

X and Y = measurements

△X and △Y = uncertainties in the measurements

76
Q

dividing two measurements with uncertainties

A

(X +- △X)/(Y +- △Y)

=
X/Y(1 +- △X/X +- △Y/Y)

77
Q

graphing measurements w/ uncertainties

A

eg. on table label it as

Time (s) +- 5s

78
Q

error bars

A

indicate the size of uncertainties

-error bars can be presented going in both axises for one dot/measurement
check slides 4

79
Q

reasons to fit a line on a graph

A
  • show a trend

- allow values to be read from our graph at a point which we did not directly measure

80
Q

interpolate

A

an estimation of a value within two known values in a sequence of values

81
Q

extrapolate

A

an estimation of a value based on extending a known sequence of values or facts beyond the area that is certainly known

82
Q

finding fit line

A

Use Least Squares Method

83
Q

Why use least squares method

A

minimises sum of squares of the vertical direction

84
Q

equation of line

A

yᵢ𝒸 = mxᵢ + c

xᵢ = particular point
yᵢₒ = observed value (measured value)
yᵢ𝒸 = calculated value from equation of line
85
Q

partial differentiation

A

know how to do it

86
Q

Derivations to learn (chap 6 of book)

A
  • least squares line fitting formula

- centroid

87
Q

standard error formula

A

slides 5

88
Q

least squares line and standard erorr

A

least squares line has smallest standard error fo all possible lines through data

89
Q

coefficient of determination

A

r², measure of how well line fits the data

-formula

90
Q

outliers

A

should never be simply discarded without justification

91
Q

assumptions of least squares line fitting method

A
  • uncertainty in independent variable is taken to be negligible
  • random uncertainty is only in dependent variable
  • uncertainty is same in each measurement. If not, use Weighted Least Squares fit
92
Q

simple way to check answer of least squares line fits

A

the centroid, which is the point given by (𝑥̅,𝑦̅), must lie on the least squares line fit.

93
Q

sig figures to report in line fit equation

A

-can use diff between measured values of y and those which are calculated using our line fit
-formulas to estimate uncertainty in m and c
-

94
Q

technical report sections

A
  • title
  • abstract
  • introduction
  • experimental method
  • results
  • discussion
  • conclusions
  • references
95
Q

abstract

A

An overview of the experiment and its findings. Why you did the experiment, what your results show and why is that significant.

96
Q

what is in an abstract

A
  • what you set out to do and why
  • how you did it
  • what you found
  • recommendations
97
Q

what is not in an abstract

A
  • introduction
  • plan of activities
  • extracts from main body with no context
  • repeat of conclusions
98
Q

introduction

A
  • Describe background + goals of experiment.
  • should place the experiment in context of what is known from existing literature.
  • Describe theory relevant to experiment.
99
Q

experimental method

A
  • be a description of what was done
  • observations of what was done, incl observations of what happened.
  • purpose: allow reader to critically examine way in which experiment was conducted + analyse results in context of what happened.
100
Q

conclusion

A
101
Q

acknowledgements

A

acknowledge assistance from colleagues through discussion, borrowing equipment or even financial support to complete the work

102
Q

scientific literature

A

Scientific literature is published in peer reviewed journals.

103
Q

peer reviewed journals

A

These are publications which release a new edition several times per year. A researcher will conduct an experiment and write a detailed document (known as a research paper) reporting the results.

104
Q

purpose of referencing

A

is expected that we will draw on the ideas and research that has gone before us. However it is expected that we will give credit to the people who have produced this knowledge that we are using. If we do not it is as if we are trying to claim their work as our own. This is plagiarism and is a very serious offence in all technical/scientific writing.

105
Q

qualitative data

A

is information that describes something. It is often subjective and responses will vary depending on the outlook of an individual. For example an individual may describe a sound as annoying or pleasant but this may or may not useful in predicting the responses of a community of people.

106
Q

quantitative data

A

data expressing a certain physical quantity, amount or range. There is a measurement unit associated with the data, e.g. metres, in the case of the height of a building