This student story was published as part of the 2025 NASW Perlman Virtual Mentoring Program organized by the NASW Education Committee, providing science journalism experience for undergraduate and graduate students.
Story by Hanna Kamperman
Mentored and edited by David Ehrenstein
While the musical triangle may be geometrically simple, its acoustic behavior is not obvious, according to new observations of the instrument’s sound wave patterns. Researchers saw hints of a new type of resonant structure in the air within the instrument’s metal frame. Many instruments, such as trumpets and violins, have enclosed spaces in which sound patterns called standing waves form at specific frequencies. But seeing such stable sound wave structures in a region that is partially open, such as that inside a triangle, is new. While the researchers need more data to be sure, they believe that the unique sound of a triangle — as compared with a straight rod — is attributable to the standing waves that the instrument generates.
Acoustics researchers want to understand how the shapes of musical instruments affect their sounds. For instruments with closed, acoustically resonant chambers, the starting point for such studies is often to analyze the standing wave patterns (called eigenmodes) that appear at specific frequencies.
The triangle, however, has no fully enclosed space, and yet it produces a sound that is different from a straight metal rod. There is no complete explanation for this sound production, since “physical triangle research is very limited,” says acoustics researcher Risako Tanigawa of Waseda University and NTT, Inc., both in Japan.
To better understand the triangle, Tanigawa and her colleagues, led by Yasuhiro Oikawa, also of Waseda, applied a sound wave imaging method that the team has developed over the past decade. The technique generates a two-dimensional visualization of the sound waves around a vibrating object with sub-millimeter resolution. It uses laser light to detect the air pressure changes and a high-speed camera to capture those changes at 1.5 million frames per second.
For each of two triangles (70 and 100 mm on a side), Tanigawa and her colleagues first used sound recordings to isolate the frequencies that were the loudest and lasted the longest after the triangle was struck. They then used their imaging technique to produce videos of the sound pressure in the air around the triangle. For each selected frequency, a unique and relatively stable acoustic pattern appeared inside the frame. Imagine the crisscrossing patterns of sunlight at the bottom of a swimming pool but more symmetrical. These patterns seemed to indicate the formation of standing waves (and thus eigenmodes) inside the triangle, despite the semi-open nature of this region of air.
To investigate further, the researchers ran simulations to find the sound frequencies at which air, bounded by rigid walls in this triangular shape, would produce such patterns. The patterns from the simulations were similar to those observed in experiments, which validated the team’s understanding of the acoustical system.
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The existence of these eigenmodes, and their ability to amplify sounds, could explain why some of the frequencies were especially loud and long-lasting, the researchers write. So this ancient instrument may survive in this shape — rather than being a straight rod — because the standing waves inside the triangle give it a distinctive sound. The team also suggests that a similar phenomenon may occur in other instruments such as tambourines and castanets.
The researchers admit that the standing waves are hard to explain theoretically, given the semi-open nature of the space. Even so, “both the results in the paper and the accompanying supplemental animations [videos] are impressive,” says Samuel Verburg, an acoustic technology expert at the Technical University of Denmark. Verburg is also optimistic about the potential of these results to popularize the use of this and other imaging technologies in the field of acoustics. Tanigawa and her colleagues believe that future musical acoustics studies using their technique will be useful for the preservation, development, and creation of musical instruments, from traditional to electronic.
Top image: A percussionist in the VU-Orchestra plays a triangle during a concert in Amsterdam. Credit: veerlebas photography. Creator: Veerle Bastiaanssen.
Hanna Kamperman
The NASW Perlman Virtual Mentoring program is named for longtime science writer and past NASW President David Perlman. Dave, who died in 2020 at the age of 101 only three years after his retirement from the San Francisco Chronicle, was a mentor to countless members of the science writing community and always made time for kind and supportive words, especially for early career writers.
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