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In an ideal gas (see The Kinetic Theory of Gases), the equation for the speed of sound is \[v = \sqrt{\frac{\gamma RT_{K}}{M}}, \label{17.6}\] where \(\gamma\) is the adiabatic index, R = 8.31 J/mol • K is the gas constant, T K is the absolute temperature in kelvins, and M is the molecular mass.
As seen in Example 16.4, the wave speed is constant and represents the speed of the wave as it propagates through the medium, not the speed of the particles that make up the medium. The particles of the medium oscillate around an equilibrium position as the wave propagates through the medium.
In my acoustics books I see $$c^2 = \frac{\mathrm{d}P}{\mathrm{d}\rho}$$ where $c$ is the speed of sound, $P$ is the pressure and $\rho$ is the density. Where does this equation come from? In my ...
Determine the speed of sound in different media; Derive the equation for the speed of sound in air; Determine the speed of sound in air for a given temperature
In summary, \(y(x, t)=A \sin (k x-\omega t+\phi)\) models a wave moving in the positive x-direction and \(y(x, t)=A \sin (k x+\omega t+\phi)\) models a wave moving in the negative x-direction. Equation \ref{16.4} is known as a simple harmonic wave function. A wave function is any function such that \(f(x, t)=f(x-v t)\).
\end{equation} This equation states that the speed of sound is some number which is roughly $1/(3)^{1/2}$ times some average speed, $v_{\text{av}}$, of the molecules (the square root of the mean square velocity).
Learning Objectives. By the end of this section, you will be able to: Explain the relationship between wavelength and frequency of sound. Determine the speed of sound in different media. Derive the equation for the speed of sound in air. Determine the speed of sound in air for a given temperature.
