Language
Country/Area
No result found
The wonderful process of sound wave deformation: How does the high-pressure phase change the speed of sound?
In the world of sound waves, a phenomenon full of mystery and beauty is quietly happening, and that is nonlinear acoustics (NLA). This branch of physics focuses on the effects that occur when the amplitude of sound waves is large enough, and reveals the subtleties of how the speed of sound changes at high pressures.
The propagation of sound waves and pressure changes
The characteristic of sound waves is that they propagate through materials as a local pressure change. When the pressure of a gas or fluid increases, its local temperature also increases, which causes the speed of sound in the compressible material to increase. As a result, a sound wave travels faster in the high-pressure phase than in the low-pressure phase.
This phenomenon has a profound impact on the frequency structure of sound waves, with the original single frequency becoming more and more like a sawtooth wave as it continues to deform.
Specifically, when an initial plane sine wave oscillates, the peak speed of the wave will be faster than the speed of the wave trough, which gradually distorts the waveform. During this process, other frequency components are also introduced, which can be described by Fourier series. This phenomenon is characteristic of nonlinear systems, since linear acoustic systems respond only to the driving frequency.
Physical analysis
Pressure changes within the medium cause wave energy to be transferred to higher harmonics. Although attenuation generally increases with increasing frequency, this effect changes the nature of the nonlinear effect with distance. The degree of nonlinearity of a material can be expressed by giving it a nonlinear parameter.
The nonlinear parameters are expressed as B / A, where A and B represent the first and second coefficients of the Taylor series expansion related to the material pressure and density.
In liquids, a modified coefficient is often used called β = 1 + B / (2A). The values of this parameter are typical of biological media. As the understanding of propagation phenomena deepens, scientists have increasingly explored nonlinear effects.
Discussion on mathematical models
To describe the behavior of nonlinear acoustics, scientists have developed a variety of mathematical equations. Among them, the Westervelt equation is one of them, which can incorporate nonlinear responses into the description of sound waves.
The Westervelt equation takes into account second-order nonlinear effects and can more comprehensively describe the behavior of sound waves in complex environments.
By studying this equation, we can understand the propagation of sound waves in nonlinear media and their characteristics as their amplitude changes. Furthermore, the Burgers equation provides a simplified one-dimensional model to study the behavior of forward-propagating waves.
Applications and phenomena
The phenomenon of nonlinear acoustics not only exists in theory, but also plays an important role in practical applications. For example, in the case of rapid sound transmission, the sonic boom phenomenon is an example. When an airplane flies at supersonic speeds, it produces a sudden sound wave, which is a change in waveform due to nonlinear effects.
The realization of acoustic levitation technology also relies on nonlinear acoustic phenomena. High-power sound waves make objects levitate in the air.
Furthermore, in medical ultrasound imaging, due to the high amplitude ratio of ultrasonic waves relative to wavelength, they show nonlinear propagation behavior, which provides a new way to improve image quality.
Thinking and the future
However, the physical behavior of music acoustics is mainly nonlinear, which makes scientists continue to seek physical modeling and synthesis methods to simulate its sound generation process. Ultimately, as scientific research continues to deepen, can we capture the nonlinear effects of sound waves in various situations?
