The equation of variation of displacement and pressure of a sound wave is given by the wave equation, which is represented as y(x,t) = A sin(kx - ωt) where y(x,t) is the displacement of the wave at position x and time t, A is the amplitude of the wave, k is the wave number, and ω is the angular frequency.
In a sound wave, displacement and pressure are directly proportional to each other. This means that as the displacement of the wave increases, the pressure also increases, and vice versa. This relationship is described by the equation P = ρc²y, where P is the pressure, ρ is the density of the medium, c is the speed of sound, and y is the displacement.
The equation of variation of displacement and pressure of a sound wave remains the same in different mediums, as long as the medium is linear and homogeneous. However, the values of A, k, and ω may change depending on the properties of the medium, such as density and elasticity.
The equation of variation of displacement and pressure can be used for all types of sound waves, as long as the waves are longitudinal and travel through a medium. This includes both audible and inaudible sound waves, such as ultrasound and infrasound.
The equation of variation of displacement and pressure is derived from the wave equation, which is a mathematical model that describes the behavior of waves. It takes into account the properties of the medium, such as density and elasticity, and the motion of the wave, represented by the sine function. By applying the wave equation to the specific case of sound waves, we can derive the equation of variation of displacement and pressure.
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