Sound Wave



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                         Like any other wave the speed of a sound wave refers to how fast the disturbance is passed from particle to particle. Since the speed of any wave depends upon the properties of the medium through which the wave is traveling, the same thing happens in the case of sound wave as well. The speed of sound wave depends upon the compressibility and inertia of the medium. If the medium has bulk modulus B and density ρ, then the speed of sound waves in that medium is:

                         The phase of matter significantly affects the elastic properties of the medium. In general, solids have the strongest interactions between particles, followed by liquids and then gases. For this reason, longitudinal sound waves travel faster in solids than they do in liquids than they do in gases. Even though the inertial factor may favor gases, the elastic factor has a greater influence on the speed (v) of a wave:

                                                 Vsolid > Vliquid > Vgas

                In a particular medium or within a single phase of matter, the inertial property of density tends to be the property which has a greatest impact on the speed of sound. A sound wave travels faster in a less dense medium as compared to a denser medium.

               The speed of sound in air also depends upon the properties of the air namely the temperature and the pressure of the medium. For sound traveling in air at normal atmospheric pressure, the relationship between the wave speed and medium temperature is:

Here, 331m/s is the speed of sound at 0oC and Tc is the temperature is degree Celsius. Using this equation one can find the speed of the sound wave at any temperature. For example, the speed of sound wave at 20oC in air medium is 343 m/s.

When the sound wave moves through air, the amount of energy passing by a given point during one period of oscillation is give by,

Here, ρ is the density of the medium, A is the cross-sectional area, ω is the frequency of the wave, smax is the amplitude of the wave and λ is the wave length of the sound wave. Now the rate of energy transfer or the power is given by,

Here, v is the speed of sound wave in air.

Now the intensity of a wave in general is defined as the power per unit area or the rate at which the energy being transported by the wave flows through a unit area A perpendicular to the direction of travel of the wave. In the present case, the intensity of sound wave is:

Thus, the intensity of a periodic sound wave is proportional to the square of the amplitude and to the square of the angular frequency.