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The mystery of sound waves: Why do they travel at different speeds in different media?
Sound waves, as a form of energy transfer, propagate through media such as air, water or solid objects based on adiabatic compression and expansion. These waves have their own characteristics, such as sound pressure, particle velocity, particle displacement, and sound intensity. The speed of sound waves is affected by the properties of the medium itself, such as density and elasticity. In air, the speed of sound is approximately 343 meters per second, in water it is 1480 meters per second, and in solids it varies depending on the material.
Understanding the propagation properties of sound waves is critical to fields as diverse as acoustics, physics, engineering, and medicine, with applications ranging from sound design, noise reduction, and diagnostic imaging.
Sound waves are mechanical waves that transfer energy through the movement of atoms and molecules. In fluids, sound waves propagate as longitudinal waves, which means that the movement of particles is parallel to the direction of wave propagation; whereas for electromagnetic waves, they propagate as transverse waves. In solids, sound waves can propagate as longitudinal and transverse waves at the same time because of the effect of shear modulus in solids.
Sound wave equation
The sound wave equation is a key equation describing the propagation of sound waves. In the one-dimensional case, the sound wave equation of sound pressure is:
∂²p/∂x² - (1/c²)∂²p/∂t² = 0
Among them, p represents the sound pressure (Pascal), x is the propagation position of the wave (m), c is the speed of sound (m/s), and t is the time (s). As for particle velocity, its equation format is similar to that of sound pressure:
∂²u/∂x² - (1/c²)∂²u/∂t² = 0
These equations show the regularity and structure of sound waves in their propagation process.
Factors affecting the speed of transmission
The propagation speed of sound waves or the speed of sound c depends on the properties of the medium through which the wave propagates. Generally, the speed of sound can be expressed by the Newton-Laplace equation as:
c = √(C/ρ)
Where C is the stiffness coefficient and ρ is the density (kg/m³). This means that when the stiffness of a material increases, the speed of sound increases, and conversely, when the density of the material increases, the speed of sound decreases.
The propagation rate of sound waves has obvious differences in different media. These differences give us various choices when applying sound waves.
The phenomenon and interference of sound waves
Sound waves exhibit a variety of phenomena such as diffraction, reflection and interference. The phenomenon of interference is the new waveform formed when two or more waves overlap. When two audio speakers send the same signal, interference of sound waves can be observed. At some locations, constructive interference occurs, doubling the local sound pressure, while at other locations it causes destructive interference, reducing the local sound pressure to zero.
The role of reflection
Sound waves can be reflected by solid surfaces. When a propagating sound wave encounters a solid surface, a reflected wave is formed. The reflected wave interferes with the incident wave, thereby generating a standing wave in the near field. In a standing wave, the pressure and particle velocity are out of phase by up to 90 degrees, which means that at some point, the pressure reaches a maximum and the particle velocity is zero.
Sound waves in layered media
When a sound wave travels through a non-uniform medium, it diffracts when it encounters impurities or interfaces between different materials. This phenomenon is similar to the refraction, absorption and transmission of light in a Bragg mirror. The concept of acoustic wave propagation through periodic media has been widely used in acoustic metamaterial engineering.
In multi-layer materials, the absorption, reflection and transmission of sound waves can be calculated using the transmission matrix method to better design the acoustic environment.
Therefore, the various phenomena of sound waves and the differences in their propagation speeds in different media are not only of great significance to scientific research, but also have a profound impact on various applications in daily life, such as music, medical imaging, etc. . When we look to the future, what new technologies and applications will the characteristics of these sound waves lead us to explore?
