Physics 1251 The Science and Technology of Musical Sound

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Physics 1251The Science and Technology of
Musical Sound

• Unit 1
• Session 4
• Thinking as a Physicist

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• Foolscap Quiz
• A ripple on the surface of the water makes a
  small piece of cork go up and down 3 times per
  second. If the distance between the ripples is
  5.3 cm, what is the velocity of the water waves?

Frequency 3 Hz Wavelength 0.053 m v f
? (3 Hz) (0.053 m) 0.16 m/s
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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• This week in lab
• Fundamentals of Waves
• frequency, velocity, wavelength, waveform
• Pick up Supplement The Speed of Sound

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• Check out the QA
• www.phys.unt.edu

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• 1' Lecture
• A Physicist ( a Natural Philosopher)
• Observes Reality
• Abstracts the significant
• Measures the observables
• Models the mathematical relationships
• Predicts the outcome and
• Compares with Reality
• The book of Nature is written in the language of
  Mathematics.
• Galileo Galilei (1564-1642)

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• Physicists ask these questions

How? How does it work?
How much? How much does the outcome change when
I change the conditions?

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• Observation is the act of perceiving, noticing
  or paying special attention to what is happening
  before you.

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• Three Errors of Observation
• First error-- inattention, misdirection
• Second error-- ignoring the obvious
• Third error-- seeing the expected

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicists

• The qiuck brown fox jumps over
• lazy dog. Now is the time
• time for all good men to come
• to the aid of there partry. Now it
• the time that tires mens soles.

Ten (10) errors on this page.
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Physics 1251 Unit 1 Session 4 Thinking as
a Physicists

• The qiuck brown fox jumps over
• (the) lazy dog. Now is the time
• time for all good men to come
• to the aid of there partry. Now it
• the time that tires mens soles.

Ten (10) errors on this page.
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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• Abstraction is the act of thinking of a quantity
  or idea apart from the particular instance or
  material object from which it was drawn.

• What are the qualities or categories that
  describe the observation?

• What is relevant/irrelevant?

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• Measurement is the act of quantitative comparison
  to a standard unit.

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• Lord Kelvin ( William Thompson)
• I often say that when you can measure what you
  are speaking about, and express it in numbers,
  you should know something about it, but when you
  cannot express it in numbers, your knowledge is
  of a meagre and unsatisfactory kind.

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• The book of Nature is written in the language of
  Mathematics.
• Galileo Galilei (1564-1642)

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• Fundamental Units
• Time second

• Originally (1/60)(1/60)(1/24)
• of mean solar day

- Currently 9 192 631 770 periods of radiation
of cesium-133 atoms
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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• Fundamental Units
• Distance meter

• Originally 1/40 000 000 circumference of
  Earth

• Currently distance light travels in 1/299 792
  458 sec

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• Fundamental Units
• Mass kilogram

• Originally the mass of 1/1000 m3 water

• Currently the mass of the standard kilogram

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• 80/20 Important Prefixes
• Mega- ( M) 1 000 000
• kilo- ( k) 1 000
• centi- ( c) 1/100
• milli- ( m) 1/1 000
• micro- ( ?) 1/1 000 000

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• Scientific Notation
• Big Numbers 1.234567 x 10 3 1234.567
• Small Numbers 1.234567 x 10 2 0.01234567

Know your calculator Enter 1.234567 EXP or
EE 03 1.234567 03 Enter 1.234567 EXP 03
/- 1.234567-03
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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• Modeling is the act of forming a hypothetical
  representation or description of a concrete
  phenomenon, often based on analogy and expressed
  in the language of mathematics.

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Physics 1251 Unit 1 Session 4 Thinking a
Physicist

• What is the approximate relationship between the
  ratio of the lengths of two simple pendula and
  the ratio of their periods?

Try P1 / P2 v (L1 /L2 )
Model P(sec) 2.007 v L (m) (2p /v g) v L
(m)
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Physics 1251 Unit 1 Session 4 Thinking a
Physicist

• Does the period of a pendulum depend on the
  amplitude of the swing?

Same Period
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Physics 1251 Unit 1 Session 4 Thinking a
Physicist

• What is the approximate relationship between the
  ratio of the lengths of two simple pendula and
  the ratio of their periods?

Length L
Period P time to complete one cycle
P ? vL
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Physics 1251 Unit 1 Session 4 Thinking a
Physicist

• Idea increase precision by measuring time for
  ten (10) oscillations (10 periods) then dividing
  by 10.

Period P (time to complete ten cycles)/10
Period 3.5 sec (single measurement)
Period (34.8 sec)/10 3.48 sec
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Physics 1251 Unit 1 Session 4 Thinking a
Physicist

• L 3.00 m 2.00 m
• 10 P 34.8 sec 28.4 sec
• P 3.48 sec 2.84 sec
• P1 /P2 1.23 L1 /L2 1.50
• v(L1 /L2) 1.22

Pendulum 1
Pendulum 2
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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• 80/20Precision is the fineness of a measurement.
• 80/20Accuracy is the correspondence of a
  measurement to an (unknown) true value.

Measurement
Less precise
Standard
Less accurate
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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• 80/20Experimental Error is the difference between
  a measurement and the (unknown) true value. One
  can only estimate the expected probable error.

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• Measurements should be reported only to the
  number of (significant) digits or figures that
  represent the accuracy and precision of the
  measurement.

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• 80/20Rules for significant figures
• Addition or subtraction Round off terms to same
  precision of least precise addend before addition
  or subtraction.
• Multiplication or division Perform operation
  then round off afterward to same number of
  significant figures as least accurate product or
  divisor.

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• Addition
• 2.345 x 103 1.2345678 x 102
• 2.345 x 103 .123 x 103 (rounded)
• 2.468 x 103

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• Multiplication
• (2.345 x 103 )x(1.2345678 x 102 )
• (2.345 x 1.2345678) x (103 x 102 )
• (2.895061491) x 1032
• 2.895 x 105 (round to 4 sig figs)

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• Prediction is the act of telling before hand what
  will happen and by how much.

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• Comparison is the act of bringing together two
  things to ascertain their agreement or divergence.

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• Poppers
• Principle of the Insufficiency of Induction
• There is never enough data to prove a proposition
  by induction.
• Only one valid disparate inductive result is
  sufficient to disprove a proposition.

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• How can I tell science from pseudo-science?

• Is it falsifiable?
• Can it be tested?
• Is there a mechanism?
• If not, it isnt science.

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• Does a magnetic mattress have physiologically
  beneficial effect?
• http//www.holistichealthtools.com/magnetic.html

• Is it falsifiable?
• Can it be tested?
• Is there a mechanism?
• If not, it isnt science.

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Physics 1251 Unit 1 Session 4 Thinking as
a Physicist

• Summary
• Observesee what is there.
• Abstractideate the significant.
• Measurecompare to standard.
• Modeluse math.
• Predictrisk a prognostication.
• Comparecheck it out.

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Physics 1251 Unit 1 Session 4i Thinking
as a Physicist

• Summary (contd.)
• Units fundamentalsecond, meter, kilogram
  derivedHz, N, Pa
• Scale Prefixes M, k, c, m, µ
• Scientific notation 1.234 x 103
• 1.234 E03 or 1.234 03
• Experimental error
• Significant figures
• Insufficiency of induction