Kyle Forinash

Time-frequency analysis with the continuous wavelet transform

The continuous wavelet transform can be used to produce spectrograms which show the frequency content of sounds (or other signals) as a function of time in a manner analogous to sheet music. While this technique is commonly used in the engineering community for signal analysis, the physics community has, in our opinion, remained relatively unaware of this development. Indeed, some find the very notion of frequency as a function of time troublesome. Here spectrograms will be displayed for familiar sounds whose pitches change with time, demonstrating the usefulness of the continuous wavelet transform.

Building real laboratories on the internet

A majority of the pedagogical uses of computers fall somewhere within the five headings of drill, number crunching, laboratory applications, simulations, and self-paced courses (Arons, 1984). In this paper, we discuss a sixth use for computerised instruction, dispersed laboratories over the internet, one which was probably unanticipated years ago when the internet and laboratory technologies were less accessible and less friendly than now. The pervasive interconnectivity of the internet provides the means for entirely new kinds of laboratory experiences for the science student. For example, students can remotely access laboratory equipment that previously would have been too expensive or too dangerous for a typical student laboratory. Large-scale collaborative experiments between students separated geographically are also possible. This paper presents an overview of the technology for science laboratories over the internet, example laboratory experiments, and potential applications.

Smartphones as portable oscilloscopes for physics labs

Given that todays smartphones are mobile and have more computing power and means to measure the external world than early PCs, they may also revolutionize data collection, both in structured physics laboratory settings and in less predictable situations, outside the classroom. Several examples using the internal sensors available in a smartphone were presented in earlier papers in this column.1, 2 But data collection is not limited only to the phones internal sensors since most also have a headphone port for connecting an external microphone and speakers. This port can be used to connect to external equipment in much the same way as the game port on the early Apple II was used in school labs. Below is an illustration using the headphone port to receive data from an external circuit: smartphones as a portable oscilloscope using commercially available hardware and applications.

Brownian motion using video capture

Although other researchers had previously observed the random motion of pollen grains suspended in water through a microscope, Robert Browns name is associated with this behaviour based on observations he made in 1828. It was not until Einsteins work in the early 1900s however, that the origin of this irregular motion was established to be the result of collisions with molecules which were so small as to be invisible in a light microscope (Einstein A 1965 Investigations on the Theory of the Brownian Movement ed R Furth (New York: Dover) (transl. Cowper A D) (5 papers)). Jean Perrin in 1908 (Perrin J 1923 Atoms (New York: Van Nostrand-Reinhold) (transl. Hammick D)) was able, through a series of painstaking experiments, to establish the validity of Einsteins equation. We describe here the details of a junior level undergraduate physics laboratory experiment where students used a microscope, a video camera and video capture software to verify Einsteins famous calculation of 1905.

Nonlinear response of the sine-Gordon breather to an a.c. driver

We investigate the nonlinear response of the continuum sine-Gordon (SG) breather to an a.c. driver. We use an ansatz by Matsuda which is an exact collective variable (CV) solution for the unperturbed SG breather and uses only a single CV, r(t), which is the separation between the center of masses of the kink and antikink that make up the breather. We show that in the presence of a driver with an amplitude below the breakup threshold of the breather into kink and antikink, the a.c.-driven SG is quite accurately described by the r(t), which is a solution of an ordinary differential equation for a one-dimensional point particle in a potential V(r) driven by an a.c. driver and with an r-dependent mass, M(r). That is below the threshold for breakup, the solution for a driven r(t) and the use of the Matsuda identity gives a solution for the a.c.-driven SG, which is very close to the exact simulation of the a.c.-driven SG. We use a wavelet transform to analyze the frequency dependence of the time-dependent nonlinear response of the SG breather to the a.c. driver. We find the wavelet transforms of the CV solution and of the simulation of the a.c.-driven SG are qualitatively very similar to each other and often agree quite well quantitatively. In cases of breakup of the breather into K and A, where there is no appreciable radiation of phonons, we find the CV solution is very close to the exact simulation result.

Simple Internet data collection for physics laboratories

We present a surprisingly simple yet flexible method for remote data collection over the Internet. The method requires minimal development effort, has considerable hardware and software independence, and is essentially free. The basic approach is to convert a scientific measurement instrument into an Internet device to give remote computers access to the instrument. The method is compatible with most programming languages and software applications that have Internet access. It can be used with many serial port measurement instruments and allows different computers, operating systems, and instruments to be intermixed when collecting data. We give three examples of how the method has been used to enhance the undergraduate physics laboratory experience.

Photogate Timing with a Smartphone

In a previous article we demonstrated that a simple, passive external circuit incorporating a thermistor, connected to a mobile device through the headset jack, can be used to collect temperature data.1 The basic approach is to output a sine wave signal to the headset port, through the circuit, and input the resulting signal from the headset microphone. By replacing the thermistor with other variable resistors, the circuit can perform other data measurements. A photoresistor in the circuit will change the amplitude of the returning signal by varying the resistance, depending upon the intensity of light reaching it. The circuit used is shown in Fig. 1 (a discussion of alternative circuits is given in Ref. 2). Two or more photoresistors can be placed in series to form multiple photogates, as shown in Fig. 2. The photoresistors used here have a resistance of about 120 kΩ in the dark and 5 kΩ under lamp light. Ordinary household lamps were used as light sources.

A first course in the history and philosophy of science

A philosopher (WR) and a physicist (KF) have been team teaching a history and philosophy of science course every other year over the past twelve years at Indiana University Southeast. Our approach has been to spend about half the semester talking about the development of the Sun-centred system of Copernicus, covering some important developments in astronomy and physics during the period from Copernicus until Newtons death. The second half of the course examines modern views of scientific method, the scope of scientific knowledge, and observations about science and values put forth by various philosophers (for example, Popper, Ziman, Thagard, Carnap, Hempel, Quine and others). Students are asked to write essays critiquing these philosophical views using historical examples from the earlier readings as support for their arguments. The last time we ran the course we placed the papers (anonymously) on the web and had participants in the class make suggestions to each other on improving the essays of their fellow students. We feel this was a valuable exercise and intend to try it again. Our paper includes a discussion of our method and a sample of issues raised.

Smartphones—Experiments with an External Thermistor Circuit

This contribution adds a further example to illustrate how to use the headphone port of a smartphone to receive data from an external circuit, in this case, a simple, adaptable homemade example for temperature measurement.1

Galileo's Mathematical Language of Nature

Undergraduate students do not always make a clear distinction between physics and mathematics, particularly early in their studies. We offer a simple historical example and show how it can be used to illustrate some of the important differences and relationships between the two. The example is Galileos treatment of motion under uniform acceleration, in which he uses geometry instead of algebra to represent quantities such as time and velocity and stresses the need to test the adequacy of the representation by experiment. The general importance of Galileos work in the history of science and the fact that it is accessible to undergraduates not concentrating their studies in mathematics or the sciences make it particularly suitable for our purposes. In addition to undergraduate courses in physics or mathematics, many of the points we make should be useful in courses in the history and philosophy of science and mathematics.