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Physics 1251 The Science and Technology of Musical Sound

Physics 1251 The Science and Technology of Musical Sound. Unit 1 Session 4 Thinking as a Physicist. Physics 1251 Unit 1 Session 4 Thinking as a Physicist. Foolscap Quiz:

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Physics 1251 The Science and Technology of Musical Sound

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  1. Physics 1251The Science and Technology of Musical Sound Unit 1 Session 4 Thinking as a Physicist

  2. 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⋅ λ= (3 Hz) (0.053 m) = 0.16 m/s

  3. 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”

  4. Physics 1251 Unit 1 Session 4 Thinking as a Physicist Check out the Q&A: www.phys.unt.edu

  5. 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)

  6. 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?

  7. 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.

  8. 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

  9. 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.

  10. Physics 1251 Unit 1 Session 4 Thinking as a Physicists The qiuck brown fox jumps over (the) lazy dog. Now is the time timefor all good men to come to the aid of therepartry. Now it the time that tiresmens’soles. Ten (10) errors on this page.

  11. 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?

  12. Physics 1251 Unit 1 Session 4 Thinking as a Physicist Measurement is the act of quantitative comparison to a standard unit.

  13. 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.”

  14. 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)

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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.

  21. 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 = √ (L1 /L2 ) Model : P(sec) = 2.007 √ L (m) = (2π /√ g) √ L (m)

  22. Physics 1251 Unit 1 Session 4 Thinking a Physicist Does the period of a pendulum depend on the amplitude of the swing? Same Period

  23. 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 ∝ √L

  24. 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

  25. 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 √(L1 /L2) : 1.22 Pendulum #1 Pendulum #2

  26. 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

  27. 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.

  28. For example: 1.24 means that the (true) value is between 1.23500000… and 1.244999999…. 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.

  29. 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.

  30. 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

  31. 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 103+2 = 2.895 x 105 (round to 4 sig figs)

  32. 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.

  33. 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.

  34. Physics 1251 Unit 1 Session 4 Thinking as a Physicist Popper’s 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.

  35. 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 isn’t science.

  36. 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 isn’t science.

  37. Physics 1251 Unit 1 Session 4 Thinking as a Physicist Summary: • Observe—see what is there. • Abstract—ideate the significant. • Measure—compare to standard. • Model—use math. • Predict—risk a prognostication. • Compare—check it out.

  38. Physics 1251 Unit 1 Session 4i Thinking as a Physicist Summary (cont’d.): • Units: fundamental—second, meter, kilogram; derived—Hz, 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

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