As pressure rises, the medium becomes less elastic (stiffer), accelerating the sound speed. The elasticity modulus for air, mentioned earlier in Equation 1, is proportional to pressure. The ratio of pressure over density is constant, bound by temperature. Equation 2 shows that pressure and density are proportional to each other when temperature is matched. For gaseous media there’s a push-pull relationship between pressure and density. The Kelvin scale is a shifted Celsius scale where 0 Kelvin, the lowest possible temperature, equals -273.15 degrees Celsius (-459.67 degrees Fahrenheit). Again I’ve singled out the relevant parameters in order to keep it simple. The pressure/density relationship for an ideal gas is shown in Equation 2, which holds as long as the medium’s thermodynamic properties, molecular composition and volume are unchanged. The air we use for acoustic transmission acts like an ideal gas (conveniently simplifying our equations). However, for air as a medium there’s a twist. The fact that pressure and density change with altitude leads to the common misconception that we’d need to set delays differently on Mt. We could therefore expect that density will play a significant part in the sound speed of air. And yet water is over 15,000 times less elastic (stiffer) than air, offsetting the comparatively small density increase, making the water sound speed more than four times faster than through air.
Equation 1 seems to indicate that the high density should decrease the medium’s sound speed, which is quite counterintuitive. At room temperature water is over 800 times more dense than air. Notice how increasing elasticity (stiffness) accelerates sound speed (higher numbers mean less elastic and more stiff) and rising density decelerates.Ĭonsider the fact that sound travels faster through water than air. ρ (Greek letter rho) is density measured in kilograms per cubic meter.K is the elasticity modulus measured in Pascal.c is the speed of sound measured in meters per second.I’ve singled out the relevant parameters to keep it simple. In general, the speed of sound through any medium (solid, liquid or gaseous) is described by Equation 1. Density is the ratio of weight to volume measured in kilograms per cubic meter. Stiffness is a metric that describes the resistance of a substance to uniform compression and is measured in Pascal, which equals 1 Newton per square meter (approximately 0.1 kilograms per square meter or 0.02 pounds per square foot). The speed of sound through a medium depends predominantly on its stiffness and density. Sound energy passes through the medium by compressing and expanding these bonds. The medium is composed of molecules held together by intermolecular forces. The speed of sound is the distance traveled per second through an elastic medium.
There are some popular misconceptions on this subject related to pressure, density, and other effects that are addressed here. However, it is primarily and more directly related to molecular speed and thus temperature than it is to anything else.In this article we’ll investigate how the speed of sound in air is, for all intents and purposes, exclusively temperature dependent within the audible bandwidth of our typical applications. One might also note that the temperature is lower as one ascends primarily because the pressure is lower as one ascends and then conclude that the speed difference is equally attributable to lower pressure (or lower density for that matter). Since molecular speed in a gas is a direct function of average molecular kinetic energy and that is a direct function of temperature, the speed of sound in a gas will also be a function of temperature.Īt the cruise altitude of the Concorde the atmospheric temperature is below that of the standard atmospheric temperature at sea level, so the speed of sound is also lower. Therefore, the sound wave can not possibly move through the gas at a speed greater than that of the individual molecules themselves, and in fact must move at a lower speed than that due to the random nature of molecular movement. A sound wave moving through a gas requires a small scale bulk movement of gas molecules back and forth as pressure at any locations builds or falls.
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