Wednesday, April 15, 2020

The acoustic alchemy of Pan Music (hollow sphere or tube): Ancient Flute and Pipes exhibits Inverse Doppler Effect as Acoustic Alchemy Metamaterial!

these metamaterials also overcome the limitations of broadband negative bulk modulus and mass density to provide a region of negative refraction and inverse Doppler effects. It was also shown that inverse Doppler effects can be detected in a flute, which has been popular for thousands of years in Asia and Europe.

In this paper, inspired by the fact that visible light comprises seven light colours and musical temperament consists of seven musical scales, a ‘flute-like’ model of an acoustic meta-cluster, containing seven meta-molecules with different dimensions was proposed.

 Using this broadband double-negative sample, we experimentally measured refractions and inverse Doppler effects from 1.186 kHz to 6.534 kHz. It was also shown that inverse Doppler effects can be detected in a flute, which has been popular for thousands of years in Asia and Europe.
 Inspired by the fact that visible light comprises seven light colours and audible sound can be divided into seven musical scales (1, 2, 3, 4, 5, 6 and 7) and several tones (A, B, C, D and so on), we construct the general broadband acoustic double-negative metamaterials by using a meta-molecule cluster set.
  Seven acoustic meta-molecules are combined to construct a cluster, and two clusters are combined to construct a cluster set. The length ratios of the units in a cluster are 1, 5/7, 4/7, 3.5/7, 3/7, 2.5/7 and 2/7; the aperture ratios in a set are 1 and 2, that is, i = 2 and j = 7.
 However, limited studies have investigated the sound effects caused by the relative movement between a flute and the audience. Considering that acoustic metamaterials composed of ‘flute-like’ meta-molecules can generate inverse Doppler effects, we hypothesised that the flute also exhibits the inverse Doppler effect.

  Oscillograms detected by the static and moving microphones of Tone 4 at the blow hole. The frequency of the source is 1079.3 Hz. When the moving microphone approaches the source, the detected frequency is reduced by 1.51 Hz; as the microphone recedes, the frequency increases by 1.26 Hz.
 
Our results reveal that musicians may consider the Doppler effect caused by these motions, that is, the effect of frequency shift between the source and the receiver. Flutes and several other wind instruments, such as the clarinet, oboe and suona horn, can be used to play dulcet music because the relationship between sounds created by these instruments and those received by the audience produce inverse Doppler effects. Although the Doppler effect was initially presented approximately 200 years ago, the property of the inverse Doppler effect has been utilised for thousands of years. Flutes may be considered as the oldest instruments associated with a negative refractive index in sound wave propagation; these instruments can be used as a basic unit of the design of various acoustic metamaterials.
 https://www.nature.com/articles/s41598-018-36517-7

Inverse Doppler Effects in Pipe Instruments

  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.
In 2001, Smith et al. first manufactured a left-handed material with periodically arranged metallic wires and split rings, and experimentally demonstrated the phenomenon of negative refraction10. Since then the research of left-handed materials boomed, resulting in electromagnetic metamaterials11,12,13,14,15 being one of the mostly studied area. In 2000, Liu et al. proposed the idea of localized resonance, which later became the foundation of acoustic metamaterials. In particular, each resonance unit - which is equivalently an artificial “meta-atom” - that constitutes the acoustic metamaterial is orders of magnitude smaller in size relative to the effective operating wavelength. The resonant frequency of each unit is primarily determined by its geometry and size. Various acoustic metamaterials with negative effective mass density were engineered by periodically arranging the acoustic “meta-atoms”16. In 2006, Fang et al. manufactured a one-dimensional acoustic metamaterial with negative effective dynamic modulus at ultrasound frequencies.
This type of metamaterial is composed of Helmholtz resonators of which the group and phase velocities are opposite in direction near the resonant frequency. It was further showed that the dynamic bulk modulus of this metamaterial calculated based on a homogeneous medium model is negative at the resonant frequency17. In our previous works, we designed two types of artificial “meta-atoms” (i.e. split hollow sphere (SHS)18,19 and hollow steel tube (HST)20,21) to achieve negative effective bulk modulus and negative mass density, respectively. Later, a double-negative acoustic metamaterial was engineered by combining these two “meta-atoms”20,22. We also designed a flute-like “meta-molecule” (i.e. perforated hollow tube (PHT)22,23) by seamlessly integrating two types of “meta-atoms” to achieve simultaneous negative bulk modulus and negative mass density.
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 The pipe instrument is one of the most popular musical instruments of all time. Flutes, as one of the earliest known instruments, dated back to 8000 years ago25, or perhaps earlier26, thanks to its simple construction, light weight and euphonious tones. Although our ancestors were unware of the operating principles of a resonator, they did notice that sound pitches produced by a flute were somehow related to the arrangement of holes as well as the instrument length. 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 now well-known that the tube length and opening manner of a flute determine its resonant frequency. However, little attention has been paid to the sound effect caused by the relative motion between a flute and the audience.





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