The integration of physics, music, and mathematics has long been used to increase students' interest and motivation in these subjects. For example, previous articles in this journal have shown how to teach physical concepts in a musical context, use a smartphone to check the resonant frequencies of whistles, use a smartphone to examine the spectra…

Creating pleasant musical sounds by vibrating the strings of musical instruments such as guitars and violins is the result of the type of instrument played as well as the mastery of the player. This article explains the physics of vibrating strings caused either by a bow drawn over them or by being plucked, and provides a simple analysis to…

This paper describes a fascinating connection between the physics of music and the famous chord in the dissonant rhythmic section of Stravinsky's "The Rite of Spring" (1913). The analysis of Stravinsky's chord will draw from the physics of harmonics, musical intervals, mathematics, and cognitive psychology. This highly interdisciplinary…

Harmonics arise naturally from the resonances in strings and pipes. A video demonstration (Ruiz 2016 "YouTube: Tuba Harmonics" (https://youtu.be/souhEzOP9c4)) is provided where a tubist (coauthor Holmes) produces a phenomenal 24 harmonics using a single tuba pipe length by controlling the buzz of his lips. The frequencies of 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…

The basic physics of the flute is presented from the perspective of a professional flutist. The flutist can control loudness, pitch and to some extent timbre. Oscilloscope images are provided to compare changes in these three fundamental sound characteristics. Readers can view a video (Ruiz 2017 "Video: The Flute"…

In a dramatic physics demonstration, a professional flutist produces four resonances with a 12 ounce Boylan soda bottle solely through her breath control. The 22cm bottle acts like a Helmholtz resonator for the lowest pitch. The three higher pitches fall near the 3rd, 5th, and 7th harmonics for a 22cm closed pipe. A video of this remarkable feat…

We have developed an online oscilloscope program which allows users to see waveforms by utilizing their computer microphones, selecting from our library of over 30 audio files, and opening any *.mp3 or *.wav file on their computers. The oscilloscope displays real-time signals against time. The oscilloscope has been calibrated so one can make…

The uniting of two seemingly disparate subjects in the classroom provides an interesting motivation for learning. Students are interested in how these subjects can possibly be integrated into related ideas. Such is the mixture of physics and music. Both are based upon mathematics, which becomes the interlocking theme. The connecting physical…

Producing a deep bass tone by striking a large 3 m (10 ft) flexible corrugated drainage pipe immediately grabs student attention. The fundamental pitch of the corrugated tube is found to be a semitone lower than a non-corrugated smooth pipe of the same length. A video (https://youtu.be/FU7a9d7N60Y) of the demonstration is included, which…

A simple pipe whistle can be made using pieces of PVC pipe. The whistle can be used to measure the resonant frequencies of open or closed pipes. A slightly modified version of the device can be used to also investigate the interesting dependence of the sound frequencies produced on the orifice-to-edge distance. The pipe whistle described here…

The physics of the plucked string has been treated in many articles and books. For our 12th-grade high school physics laboratory, we have built a cheap, simple sonometer apparatus for each pair of students on which they may investigate some interesting phenomena that arise when a string is plucked. Among these are the generation of harmonics…

The simultaneous sound of several voices or instruments requires proper tuning to achieve consonance for certain intervals and chords. Most instruments allow enough frequency variation to enable pure tuning while being played. Keyboard instruments such as organ and piano have given frequencies for individual notes and the tuning must be based on a…

A simple geometric construction giving acceptable approximations to the locations of twelve points for placing frets on a guitar is described both geometrically and analytically. (DT)

Describes an empirical method for tuning a piano by matching measured fundamental frequencies to values determined using a pocket calculator. (Author/GA)