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

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 = m Frequency = 3 Hz; Wavelength = m v = f ⋅ λ= (3 Hz) (0.053 m) = 0.16 m/s

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”

Physics 1251 Unit 1 Session 4 Thinking as a Physicist Check out the Q&A:

Physics 1251 Unit 1 Session 4 Thinking as a Physicist 1′ Lecture: A Physicist ( a Natural Philosopher) A Physicist ( a Natural Philosopher) Observes RealityObserves Reality Abstracts the significantAbstracts the significant Measures the observablesMeasures the observables Models the mathematical relationshipsModels the mathematical relationships Predicts the outcome andPredicts the outcome and Compares with RealityCompares with Reality “The book of Nature is written in the language of Mathematics.” “The book of Nature is written in the language of Mathematics.” Galileo Galilei ( )

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?

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.

Physics 1251 Unit 1 Session 4 Thinking as a Physicist Three Errors of Observation: First error-- inattention, misdirection First error-- inattention, misdirection Second error-- ignoring the obvious Second error-- ignoring the obvious Third error-- seeing the expected Third error-- seeing the expected

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.

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.

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 are the qualities or categories that describe the observation? What is relevant/irrelevant?What is relevant/irrelevant?

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

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.”

Physics 1251 Unit 1 Session 4 Thinking as a Physicist “The book of Nature is written in the language of Mathematics.” Galileo Galilei ( )

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: periods of radiation of cesium-133 atoms

Physics 1251 Unit 1 Session 4 Thinking as a Physicist Fundamental Units: Distance: meter - Originally: 1/ circumference of Earth - Currently: distance light travels in 1/ sec

Physics 1251 Unit 1 Session 4 Thinking as a Physicist Fundamental Units: Mass: kilogram - Originally: the mass of 1/1000 m 3 water - Currently: the mass of the standard kilogram

Physics 1251 Unit 1 Session 4 Thinking as a Physicist 80/20 Important Prefixes: Mega- ( M) = kilo- ( k) = centi- ( c) = 1/100 milli- ( m) = 1/1 000 micro- (  ) = 1/

Physics 1251 Unit 1 Session 4 Thinking as a Physicist Scientific Notation Big Numbers: x 10 3 = Small Numbers: x 10 –2 = Know your calculator: Enter: “ EXP” or “EE” “03” : Enter: “ EXP 03 +/-” :

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.

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 P 1 / P 2 = √ (L 1 /L 2 ) Model : P(sec) = √ L (m) = (2π /√ g) √ L (m)

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

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

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 = (34.8 sec)/10 = 3.48 sec Period = 3.5 sec ( single measurement)

Physics 1251 Unit 1 Session 4 Thinking a Physicist L:3.00 m 2.00 m 10 P:34.8 sec28.4 sec P:3.48 sec2.84 sec P 1 /P 2 :1.23 L 1 /L 2 : 1.50 √(L 1 /L 2) : 1.22 Pendulum #1 Pendulum #2

Physics 1251 Unit 1 Session 4 Thinking as a Physicist 80/20 Precision is the fineness of a measurement. 80/20 Accuracy is the correspondence of a measurement to an (unknown) true value. Less precise Less accurate Standard Measurement

Physics 1251 Unit 1 Session 4 Thinking as a Physicist 80/20 Experimental Error is the difference between a measurement and the (unknown) true value. One can only estimate the expected probable error.

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

Physics 1251 Unit 1 Session 4 Thinking as a Physicist 80/20 Rules for significant figures: Addition or subtraction: Round off terms to same precision of least precise addend before addition or subtraction. 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. Multiplication or division: Perform operation then round off afterward to same number of significant figures as least accurate product or divisor.

Physics 1251 Unit 1 Session 4 Thinking as a Physicist Addition: Addition: x x 10 2 = x x 10 3 (rounded)= x 10 3

Physics 1251 Unit 1 Session 4 Thinking as a Physicist Multiplication: Multiplication: (2.345 x 10 3 )x( x 10 2 )= (2.345 x ) x (10 3 x 10 2 ) = ( ) x = x 10 5 (round to 4 sig figs)

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.

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.

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. There is never enough data to prove a proposition by induction. Only one valid disparate inductive result is sufficient to disprove a proposition. Only one valid disparate inductive result is sufficient to disprove a proposition.

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.

Physics 1251 Unit 1 Session 4 Thinking as a Physicist Does a magnetic mattress have physiologically beneficial effect? Is it falsifiable? Can it be tested? Is there a mechanism? If not, it isn’t science.

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

Physics 1251 Unit 1 Session 4i Thinking as a Physicist Summary (cont’d.): Units: fundamental—second, meter, kilogram; derived—Hz, N, Pa Units: fundamental—second, meter, kilogram; derived—Hz, N, Pa Scale Prefixes: M, k, c, m, μ Scale Prefixes: M, k, c, m, μ Scientific notation: x 10 3 Scientific notation: x 10 3 [1.234 E03 or ] Experimental error Experimental error Significant figures Significant figures Insufficiency of induction Insufficiency of induction