Wave equation for sound waves

In summary, the conversation discussed the proof of the wave equation for a sound wave in a medium, and how it can be used to find the excess pressure at any point in time. It was noted that the pressure at a specific point may change due to the displacement of the surrounding material, causing a discrepancy in the pressure calculated using the bulk modulus equation.
  • #1
pardesi
339
0
i saw the 'proof' of the wave equation for a sound wave in a medium assuming the wave equation for a dissplacement wave.
that is the equtaion [tex] s=s_{0} \sin(kx-wt)[/tex] is supposed to hold for all points for a wave propagating in the x direction.
then using this he found out the excess pressure at any point [tex]x[/tex] a any time [tex] t [/tex].
well what he did was let at time t=0 wave started and at time t say the dislpacement of any point x be s and that of [tex]x+\delta x[/tex] be [tex]s+ \delta s[/tex].then we have
change in volume [tex]\delta V=-A\delta s=-Ak \cos(kx-wt) \delta x[/tex]
hence he said excess pressure on the material at x is [tex]\delta P=\frac{-B \delta V}{V}[/tex]
but my question is the fluid at x is no more at x but rather at x+s so how come the pressure calculated from the bulk modulus equtaion is that at x
 
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  • #2
He is considering the region between x and ##x+\delta x##.
 

1. What is the wave equation for sound waves?

The wave equation for sound waves is a mathematical representation that describes the behavior and propagation of sound waves in a medium. It is written as: v = λf, where v is the speed of sound, λ is the wavelength, and f is the frequency of the sound wave.

2. How is the wave equation for sound waves derived?

The wave equation for sound waves is derived from the fundamental principles of wave motion, such as the principle of superposition and conservation of energy. It can also be derived from the Navier-Stokes equations, which describe the motion of fluids.

3. What are the variables in the wave equation for sound waves?

The variables in the wave equation for sound waves are speed of sound (v), wavelength (λ), and frequency (f). These variables are all interrelated and affect the behavior of the sound wave.

4. How does the wave equation for sound waves relate to the properties of the medium?

The wave equation for sound waves is directly related to the properties of the medium through which the sound wave is traveling. The speed of sound, wavelength, and frequency are all affected by the properties of the medium, such as density, temperature, and elasticity.

5. What are some real-life applications of the wave equation for sound waves?

The wave equation for sound waves has many practical applications, such as in the fields of acoustics, music, and engineering. It is used to design and analyze musical instruments, acoustic systems, and communication devices. It is also essential in understanding the behavior of sound in different environments, such as in air, water, or solids.

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