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.
..................................
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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