Dependence on the properties of the medium

The speed of sound is variable and depends on the properties of the substance through which the wave is travelling. In solids, the speed of longitudinal waves depend on the shear deformation under shear stress (called the shear modulus), and the density of the medium. Compression waves in solids depend on the same two factors with the addition of a dependence on compressibility. In fluids, only the medium's compressibility and density are the important factors, since fluids do not tolerate shear stresses. In heterogeneous fluids, such as a liquid filled with gas bubbles, the density of the liquid and the compressibility of the gas affect the speed of sound in an additive manner, as demonstrated in the hot chocolate effect. In gases, adiabatic compressibility is directly related to pressure through the heat capacity ratio (adiabatic index), and pressure and density are inversely related at a given temperature and composition, thus making only the latter independent properties (temperature, molecular composition, and heat capacity ratio) important. In low molecular weight gases, such as helium, sound propagates faster compared to heavier gases, such as xenon (for monatomic gases the speed of sound is about 75% of the mean speed that molecules move in the gas). For a given ideal gas the sound speed depends only on its temperature. At a constant temperature, the ideal gas pressure has no effect on the speed of sound, because pressure and density (also proportional to pressure) have equal but opposite effects on the speed of sound, and the two contributions cancel out exactly. In a similar way, compression waves in solids depend both on compressibility and density—just as in liquids—but in gases the density contributes to the compressibility in such a way that some part of each attribute factors out, leaving only a dependence on temperature, molecular weight, and heat capacity ratio (see deriva ions below). Thus, for a single given gas (where molecular weight does not change) and over a small temperature range (where heat capacity is relatively constant), the speed of sound becomes dependent on only the temperature of the gas. In non-ideal gases, such as a van der Waals gas, the proportionality is not exact, and there is a slight dependence of sound velocity on the gas pressure. Humidity has a small but measurable effect on sound speed (causing it to increase by about 0.1%-0.6%), because oxygen and nitrogen molecules of the air are replaced by lighter molecules of water. This is a simple mixing effect. The Hot Chocolate Effect also known as the Allassonic Effect is a phenomenon of wave mechanics first documented in 1982 by Frank Crawford, where the pitch heard from tapping a cup of hot liquid rises after the addition of a soluble powder.[1][2] It was first observed in the making of hot chocolate or instant coffee, but also occurs in other situations such as adding salt to supersaturated hot water or cold beer. Recent research has found many more substances which create the effect, even in initially non-supersaturated liquids[3] It can be observed by pouring hot milk into a mug, stirring in chocolate powder, and tapping the bottom of the mug with a spoon while the milk is still in motion. The pitch of the taps will increase progressively with no relation to the speed or force of tapping. Subsequent stirring will gradually decrease the pitch again. Upon initial stirring, entrained gas bubbles reduce the speed of sound in the liquid, lowering the frequency. As the bubbles clear, sound travels faster in the liquid and the frequency increases. The phenomenon is explained by the effect of bubble density on the speed of sound in the liquid. The note heard is the frequency of a standing wave where a quarter wavelength is the distance between the base of the mug and the liquid surface.