Lecture 9

“We run this company on questions, not answers.” Eric Schmidt CEO of Google

“The wise man doesn't give the right answers, he poses the right questions.” Claude Levi-Strauss, French anthropologist (1908-2009).

“He who asks a question is a fool for five minutes; he who does not ask a question remains a fool forever.” Chinese Proverb

This is a sampling of comments about questioning over a large span of time in human history (the middle comment is by an expert in human cultures).

Questioning based on models, heuristics, patterns: Show first part of the video by Sean Carroll about the nurse who was convicted of murdering children. The jury wanted a cause of these deaths when it was just a statistical correlation no causation. The jury needed a cause so she was the cause and needed to be put away. We all want a model of how the way the world works but often things occur just by chance (there will be a chance you will get three 6’s when you roll three dice. No cause-effect relationship however).

[1]

Comments or questions on the video?

The questions you ask in class are related to these models.

Review of “How to lie with statistics:” List the questions the authors wants you to ask with the questioning categories (chapter 10): [2] who says so (item 1: reliable source or citations and/or item 3: how to spot bias)? how does he know (item 7: understanding different kinds of evidence)? what's missing (item 4: how to spot an assumption)? did somebody change the subject (item 5: logical fallacy)? does it make sense (item 4: how to spot an assumption and from the definition of critical thinking: interpret whether conclusions are warranted based on given data)? INCONGRUOUS. To clarify seeming violations of a model or understanding of how the world functions, CONGRUOUS. To gather information on how to apply your understanding. MODIFYING. GENERALIZING / ANALOGY. To search for similar patterns in one’s understanding. CAUSAL / CREATIVE. To generate novel patterns or improve on existing understanding. INFORMATIONAL

On the back of the questioning handout please answer this question. How are the questions from “How to lie with statistics” related to the questioning categories we use in class?

Ans: The difference is that in the book someone is trying to convince you that their model of the (often societal like we should build more nuclear reactors) world is valid (often via statistics about the way we behave). They use statistics, emotional arguments, or rhetoric to convince you. [3] You need to logically judge the validity of these arguments (the science of how you make decisions based on system 1 and system 2 thinking and the source often takes advantage of your lack of logical thinking).

My focus is on creating an understanding the way the physical world works by thinking critically about models and constructing new models. The informational category of questions is similar to the questions listed for critical thinking in “How to lie with statistics”: How do you know that? Why did you move all the balls together? However, these are now related to a physical system. The information questions become: What assumptions are made in RC decay? What is different between these two types of questions deals with being creative to generate new products, solutions, or patterns to understand the world in asking incongruous, modifying questions such as what would happen if . . .? analogy questions such as how is this similar to . . . ? or causal creative questions such as could this be caused by . . . ?

There is no hierarchy in these question categories. One type is not better than another (unlike . The author here is not trying to understand a model of the way the world works but rather trying to understand if the model a person is trying to promote is valid.

Demonstration: interference using two speakers

Superposition of waves with different frequencies. Demo of two speakers driven at different frequencies. Students use cell phone app to look in the frequency domain of the superposed sound wave. They should measure these audio frequencies on the phone (needed for the lab). Notice beats if the freq are near each other. Use your cell phones to measure the spectrum of these two speaker outputs from this web page. [4]

[5]

What is different for square law detectors vs field detectors. If the detector measured intensity then the output would be a cos^2 rather than cos function of the path difference. Would a Fourier transform of these outputs would be different? See Mathematica notebook DopplerPhaseSlideShow to show both still yield same time between fringes.

What does your ear detect?

How does the ear respond to these waves (like the microwave detector)? The sound wave is a compressional pressure variation which moves a membrane (ear drum or drum attached to magnetic which moves through a coil to generate an emf) [6] So the response is to the pressure (amplitude of the wave) not intensity pressure squared. However, you often see this response plotted in terms of intensity or the output of a detector is calibrated to intensity (it squares the voltage from the sensor). Log plots Read this first [7]

https://en.wikipedia.org/wiki/Psychoacoustics http://www3.nd.edu/~atassi/Teaching/ame553/Notes/Sound_power.pdf http://www.pcb.com/microphonehandbookfiles/microphone_handbook_lowres.pdf

Questioning exercise: nonlinear behavior of a speaker First show superposition of acoustic waves to see if their phone spectrum analyzer works. Then drive on speaker hard by just turning up the amplifier rather than changing the waveform generator. Ask for questions.

incongruous : how can new frequencies be generated by just increasing the amplitude. Doesn’t this violate energy conservation in quantum since the energy is h freq? Congruous: Modifying: would this happen with a more expensive speaker? Analogous: Is this like making an ocean wave getting large enough to break (it involves the speaker and not the medium)?

causal /creative: Does this happen in a quantum system?

Informational: Are the different frequencies integral multiples of the driving frequency?

Show the graphs of linear vs nonlinear behavior in this lecture [8]

Show that Fourier analysis of this distorted waveform requires harmonics at the fundamental.

Show the difference between linear distortion via filtering (which doesn’t generate new harmonics) and nonlinear effects [9] A filter affects harmonic components but does not generate new harmonic components. https://en.wikipedia.org/wiki/Horn_loudspeaker http://hyperphysics.phy-astr.gsu.edu/hbase/audio/spk.html

Show this thesis on modeling a speaker (illustration of what is done in grad school) http://publications.lib.chalmers.se/records/fulltext/126003.pdf

Drive one speaker hard to generate harmonics due to nonlinear effects in the speaker. Sketch membrane motion vs applied current. Fourier analyze the distorted motion (which generates a distorted acoustic wave pressure) to see the higher harmonics. This is another example of the simple model not matching reality.

Which of the labs you have done has a nonlinear behavior? The I-V curve of the microwave point contact diode is another example of nonlinear response. Sketch the I-V curve and not that V = E s so this could be an I-E plot. Now E is the EM field oscillating at 10^10 Hz. The current out of the diode then is rectified and distorted by the nonlinear response for small E. The scope sees a time average of this distorted waveform whose peak depends on E^2 or the power. For higher E field the response is approximately linear. That is an increase in E leads to a linear increase in the rectified waveform and its average value increases linearly. Graphs of Vdetector vs time allow you to see this dual behavior (E and I response) while chi squared just gives you a number. (Conservation laws just give an answer with no reason and therefore little understanding).

Paper on measuring g to relate LCR expt to doppler expt. Relate this to the doppler expt. Corner cube mirror is used to mitigate rotation of the mirror when it falls. Emphasize the working eqn for “g”and the lack of derivations. Note that m1 fringes are counted in a time t1. Look at the figure of the electronics where a counter is started on a zero level crossing and stopped after m1 fringes to yield the time interval during m1 fringes just like the LRC lab. Notice the simple statistics used. No chi squared. Signal to noise goes as sqrt[N], where N is the number of photons per second (we derived noise to signal goes as 1/sqrt[N] so this ratio gets smaller with increasing N and inverting this the signal get larger wrt the noise as sqrt[N]). [http://ieeexplore.ieee.org/document/1074413/ ]