In this paper we present a pedagogical strategy to introduce the Heisenberg uncertainty principle to high school students. The basis on which this proposal relies is the Fourier transform, connecting the quantum function in the x domain, ?(x), with the function in the wave number domain, A(k). This mathematical relationship directly leads to the…

The French horn is used to introduce the three basic properties of periodic waves: amplitude, frequency, and waveform. These features relate to the perceptual characteristics of loudness, pitch, and timbre encountered in everyday language. Visualizations are provided in the form of oscilloscope screenshots, spectrograms, and Fourier spectra to…

A spectrogram of a singer's vibrato presents a striking way to introduce students to frequency, Fourier spectra, and modulation. Vibrato is discussed from the perspectives of the physicist and the musician. A dramatic spectrogram is included where coauthor soprano Michel suppresses her vibrato so that acoustical characteristics can be compared to…

This article deals with a brief biographical sketch of Joseph Fourier, his first celebrated work on analytical theory of heat, his first great discovery of Fourier series and Fourier transforms. Included is a historical development of Fourier series and Fourier transforms with their properties, importance and applications. Special emphasis is made…

What follows is a description of a demonstration of superposition of waves and Fourier analysis using a set of four tuning forks mounted on resonance boxes and oscilloscope software to create, capture and analyze the waveforms and Fourier spectra of musical intervals.

This paper presents a set of laboratory classes to be taught as a part of a 1 year calculus-based physics class. It is composed of 7 modules designed to bring together experiments and computer simulations. Each module uses both simulations and experiments to address a phenomenon under study, and lasts for 3 weeks (21 weeks total for the whole…

In this paper I discuss the motivation behind using an introduction to Fourier series as a method to unify the topics of integration techniques and series calculations in a Calculus II course.

A multi-instrument approach has been applied to the efficient identification of polymers in an upper-division undergraduate instrumental analysis laboratory course. Attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR) is used in conjunction with differential scanning calorimetry (DSC) to identify 18 polymer samples and…

Students in introductory physics courses encounter harmonics when they study standing waves on strings and in pipes. The Fourier spectrum, which plots amplitude against harmonic number, can describe all periodic tones imaginable. However, most sounds are aperiodic and therefore have additional spectral components. A real-world application that…

To understand critical problems associated with solid waste and its consequences for the environment, a laboratory experiment is presented on the synthesis of aluminum-based metal-organic framework (MOF) MIL-53(Al) from household waste (PET bottles and aluminum foil/can), for undergraduate students of chemistry. This work is designed to teach…

This paper shows the results of the epistemological and didactical analysis of the sense of variation of functions. Specifically, on the conceptions of growth and decay in a function that underlie the demonstrations of the theorem that links the sign of "f" with the sense of variation of "f". The epistemological approach…

A research-style laboratory experiment composed of the synthesis of MOF-74 materials, related structural characterization, and the cutting-edge application of electrocatalytic oxygen evolution reaction (OER) has been designed toward advanced undergraduates at East China University of Technology (ECUT). The desired monometallic MOF-74 (Ni-MOF-74…

This article outlines the theoretical rationale and process for an integrated-science approach to teaching sensation and perception (S&P) to undergraduate psychology students that may also serve as an integrated-science curriculum. The course aimed to introduce the interdisciplinary evolution of this psychological field irrespective of any…

We present a theoretical approach to the problem of the transition from Calculus to Analysis within the undergraduate mathematics curriculum. First, we formulate this problem using the anthropological theory of the didactic, in particular the notion of praxeology, along with a possible solution related to Klein's "Plan B": here,…

Fourier transforms are used widely in chemistry and allied sciences. Examples include infrared, nuclear magnetic resonance, and mass spectroscopies. A thorough understanding of Fourier methods assists the understanding of microscopy, X-ray diffraction, and diffraction gratings. The theory of Fourier transforms has been presented in this "Journal",…