Abstract
Music is older than language, and for most of human history music holds our culture together. The pipe instrument is one of the most popular musical instruments of all time. Built on the foundation of previous flute and flute-like acoustic metamaterial models, we herein report the experimental results of the inverse Doppler effects discovered in two common pipe instruments - recorder and clarinet. Our study shows that the inverse Doppler effects can be detected at all seven pitches of an ascending musical scale when there is a relative motion between a microphone (observer) and abovementioned two pipe instruments (source). The calculated effective refractive indices of these two pipe instruments are negative and varying across a set of pitches, exhibiting a desired characteristic of broadband acoustic metamaterials. This study suggests that recorder and clarinet may be the earliest man-made acoustic metamaterials known so far, offering a new explanation why pipe instruments have enjoyed wide popularity in Europe and Asia over the past hundreds and thousands years. This newly discovered phenomenon would also offer a clue into designing next-generation smart broadband double-negative acoustic metamaterials with varying refractive index.
Highlights
The Doppler effect is a fundamental phenomenon in wave propagation
Inspired by the recent findings in flute and flute-like acoustic metamaterials, we systematically studied the inverse Doppler effects of the recorder and clarinet at seven sound pitches of an ascending musical scale
The experimental results show that, the detected acoustic signals produced by these two pipe instruments shift towards lower frequencies when the observer approaching the source, whereas higher frequencies are received as the observer departing from the source
Summary
The Doppler effect is a fundamental phenomenon in wave propagation. In 1843, Doppler first generalized the change in frequency of a wave for an observer moving relative to its source[1,2]. In 2006, Fang et al manufactured a one-dimensional acoustic metamaterial with negative effective dynamic modulus at ultrasound frequencies. The materials used to make flutes have evolved from ancient animal femurs to bamboo/metal in modern days, and their manufacturing process has become fairly sophisticated It is well-known that the tube length and opening manner of a flute determine its resonant frequency. The inverse Doppler effects were observed at all seven pitches (corresponding to an ascending musical scale) produced by either the blow hole or finger holes of the flute, in spite of their differences in sound intensity and frequency. The aim is to expand our previous conclusion about the attractive metamaterial properties of a flute into other popular pipe instruments This generalization would provide a new direction for designing the basic units of generation smart broadband acoustic metamaterials
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