The air molecules oscillate in simple harmonic motion about their equilibrium positions, as shown in part (b). As the speaker moves in the negative x-direction, the air molecules move back toward their equilibrium positions due to a restoring force. As the speaker moves in the positive x-direction, it pushes air molecules, displacing them from their equilibrium positions. In solids, sound waves can be both transverse and longitudinal.)įigure 17.3(a) shows the compressions and rarefactions, and also shows a graph of gauge pressure versus distance from a speaker. (Sound waves in air and most fluids are longitudinal, because fluids have almost no shear strength. These compressions (high-pressure regions) and rarefactions (low-pressure regions) move out as longitudinal pressure waves having the same frequency as the speaker-they are the disturbance that is a sound wave. But a small part of the speaker’s energy goes into compressing and expanding the surrounding air, creating slightly higher and lower local pressures. As the speaker oscillates back and forth, it transfers energy to the air, mostly as thermal energy. In Figure 17.3, a speaker vibrates at a constant frequency and amplitude, producing vibrations in the surrounding air molecules. When the resonant frequency is reached, the glass shatters.Ī speaker produces a sound wave by oscillating a cone, causing vibrations of air molecules. As the frequency of the sound wave approaches the resonant frequency of the wine glass, the amplitude and frequency of the waves on the wine glass increase. The conditions for this relationship are that the sound propagation process is adiabatic and that the gas obeys the ideal gas law.This video shows waves on the surface of a wine glass, being driven by sound waves from a speaker. Using the ideal gas law PV = nRT leads to So that the derivative of pressure P with respect to volume V can be taken. The bulk modulus can therefore be reformulated by making use of the adiabatic condition in the form The adiabatic assumption for sound waves just means that the compressions associated with the sound wave happen so quickly that there is no opportunity for heat transfer in or out of the volume of air. When a sound travels through an ideal gas, the rapid compressions and expansions associated with the longitudinal wave can reasonably be expected to be adiabatic and therefore the pressure and volume obey the relationship The speed of sound for a uniform medium is determined by its elastic property ( bulk modulus) and its density So the detailed modeling of the effect of water vapor on the speed of sound would have to settle on an appropriate value of γ to use. However, the assumption of an adiabatic constant of γ = 1.4 used in the calculation is based upon the diatomic molecules N 2 and O 2 and does not apply to water molecules. A revised average molecular weight could be calculated based on the vapor pressure of water in the air. The calculation above was done for dry air, and moisture content in the air would be expected to increase the speed of sound slightly because the molecular weight of water vapor is 18 compared to 28.95 for dry air. This leads to a commonly used approximate formula for the sound speed in air:įor temperatures near room temperature, the speed of sound in air can be calculated from this convenient approximate relationship, but the more general relationship is needed for calculations in helium or other gases. 004 kg/mol, so its speed of sound at the same temperature isĭoing this calculation for air at 0☌ gives v sound = 331.39 m/s and at 1☌ gives v sound = 332.00 m/s. For the specific example of dry air at 20☌, the speed of sound in air is 343 m/s, while the rms speed of air molecules is 502 m/s using a mean mass of air molecules of 29 amu.įor helium, γ = 5/3 and the molecular mass is. It is interesting to compare this speed with the speed of molecules as a result of their thermal energy. The speed of sound is v sound = m/s = ft/s = mi/hr. γ = the adiabatic constant, characteristic of the specific gasįor air, the adiabatic constant γ = 1.4 and the average molecular mass for dry air is 28.95 gm/mol.M = the molecular weight of the gas in kg/mol.R = the universal gas constant = 8.314 J/mol K,.The speed of sound in an ideal gas is given by the relationship
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