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The phase velocity is the rate at which the phase of the wave propagates in space. The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.
In physics, the acoustic wave equation is a second-order partial differential equation that governs the propagation of acoustic waves through a material medium resp. a standing wavefield. The equation describes the evolution of acoustic pressure p or particle velocity u as a function of position x and time t. A simplified (scalar) form of the ...
The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics.
Though ancient Chinese, Indians, Egyptians and Mesopotamians are known to have studied the mathematical principles of sound, [2] the Pythagoreans (in particular Philolaus and Archytas) [3] of ancient Greece were the first researchers known to have investigated the expression of musical scales in terms of numerical ratios, [4] particularly the ratios of small integers.
In air at atmospheric pressure, these represent sound waves with wavelengths of 17 meters (56 ft) to 1.7 centimeters (0.67 in). Sound waves above 20 kHz are known as ultrasound and are not audible to humans. Sound waves below 20 Hz are known as infrasound. Different animal species have varying hearing ranges, allowing some to even hear ultrasounds
The fraction of sound absorbed is governed by the acoustic impedances of both media and is a function of frequency and the incident angle. [2] Size and shape can influence the sound wave's behavior if they interact with its wavelength, giving rise to wave phenomena such as standing waves and diffraction.
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The answer is affirmative, if the flow satisfies certain basic assumptions. In particular, if ρ ≪ ρ 0 {\displaystyle \rho \ll \rho _{0}} and p ≪ p 0 {\displaystyle p\ll p_{0}} , then the assumed relation follows directly from the linear theory of sound waves (see, e.g., the linearized Euler equations and the acoustic wave equation ).