Speed of sound in humid air: Accurate thermodynamic model and experimental validation

Experiments that measure the speed of sound in air are common in high schools and colleges. In the Kundt's tube experiment, a horizontal air column is adjusted until a resonance mode is achieved for a specific frequency of sound. When this happens, the cork dust in the tube is disturbed at the displacement antinode regions. The location of the displacement antinodes enables the measurement of the wavelength of the sound that is being used. This paper describes a design that uses a speaker instead of the traditional aluminum rod as the sound source. This allows the use of multiple sound frequencies that yield a much more accurate speed of sound in air.

The determination of the speed of sound in air is a classical experiment, usually performed with a resonance tube apparatus. The measured value can be checked against Eq. (1), which describes the temperature dependence of the speed of sound in dry air. A modern implementation of this speed of sound investigation uses an Arduino Uno microcontroller board, an HC-SR04 ultrasonic distance sensor, and a DS18B20 temperature sensor. The distance sensor’s transmitter produces a burst of eight ultrasonic rectangular pulses that travel through the air, reflect on an object placed in front at a distance d, and then return to the sensor’s receiver after an echo time t. This Arduino investigation, unfortunately, is harder to perform than one might expect after a first reading of Ref. 1 or 2. In this article we discuss some sources of experimental errors that can complicate this laboratory activity, and we describe some important steps that must be included in the data collection and analysis procedure, in order to obtain successful results every time.

The determination of the differences (T–T90) between the thermodynamic temperature T and the international temperature scale of 1990 (ITS-90) T90, is important for an evaluation of the approximation to T by T90. Such evaluations are necessary for the potential revision of ITS-90. A number of efforts have been devoted to the determination of (T–T90) by the acoustic gas thermometry (AGT) using spherical or quasi-spherical resonators. We report in this paper a new study in the temperature range from 234 K to 303 K using AGT in argon with a cylindrical resonator. Piezo-electric acoustic transducers were used to measure the acoustic resonant frequencies. The resonant frequencies of the transverse magnetic microwave modes of the cavity were measured using straight probe antennas. This work further illustrates the high performance of the microwave resonant procedure to measure the thermal expansion of a cylindrical cavity at different temperatures and pressures. The (T–T90) measurements, with standard uncertainties in the range from 0.5 mK to 0.8 mK, agree well with the existing data from AGT with spherical or quasi-spherical resonators. We believe that cylindrical acoustic gas thermometry, with an uncertainty comparable with that using spherical or quasi-spherical resonators but simpler mechanical assembly, has the potential for accurate measurements of (T–T90) at higher temperatures.

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This paper describes a simple experiment that students can do at home to determine the speed of sound in air. A set of audio files with selected frequencies is first created and stored on the student's computer. Resonances are obtained in a straight pipe partially inserted into a bucket of water. The length of the air-filled part of the pipe is changed by raising and lowering the pipe. Resonances are detected by ear. We present some typical results obtained by students at home. All are in good agreement with the expected value.

Standing waves are a naturally arising phenomenon in many situations where sound waves propagate in an enclosed medium. Inspired by problem 17 from the International Young Naturalists Tournament (2021), this investigation aims to establish a relationship between the speed of sound in air as a function of air temperature at constant pressure and humidity. This goal is achieved by exploiting certain properties of standing sound waves in a tube, sealed off at one end. By varying the length of the tube and the temperature of the air inside, properties of the air, such as its molar mass, can also be determined.

Although schools commonly teach that sound waves propagate faster in solids than in liquids and in liquids than in gases, there is no low-cost activity that allows students to investigate if this statement is true or not. Indeed, some existing techniques simply allow them to identify the speed of sound in air and its temperature dependence.

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Computer Measurement of the Speed of Sound in Air(My Idea)

The Speed of Sound in Air

In a high-temperature gas, the speed of sound depends upon the chemical composition, sound frequency, and chemical reaction rates. Two limiting sound speeds are normally distinguished: that of ``frozen'' or constant chemical composition, and the ``equilibrium'' sound speed. Equations to determine these two sound speeds are presented for a nitrogen-oxygen system and numerical data are presented for conditions behind a normal shock in air to a speed of Mach 20.

In the past decade, spherical acoustic resonators have proved to be useful tools for high‐accuracy measurements of the speed of sound in gases. Applications include thermophysical property determinations, acoustic thermometry, and the recent redetermination of the gas constant. The complex resonance frequencies of the resonator are described by a theoretical model that includes the effects of the viscous and thermal boundary layers, shell motion, imperfect spherical geometry, and other, less important, effects. The theoretical model is tested by comparing the consistency of speed‐of‐sound determinations using different modes, and by comparing the resonance half‐widths with the theoretical predictions. The current level of agreement of experiment and theory will be reviewed.

The expected influence of humidity on the speed of sound in standard atmospheric air at various temperatures is presented. The prediction is based on theoretical [G.S.K. Wong and T.F.W. Embleton, J. Acoust. Soc. Am. 76, 555–559 (1984)] and experimental [G.S.K. Wong and T.F.W. Embleton, J. Acoost. Soc. Am. Suppl. 1 76, S65 (1984)] data obtained for the variation of the ratio of specific heats γ in humid air. Over a temperature range from 0° to 30 °C, the maximum uncertainty on the sound speed ratio ch/c0, is estimated to be less than 400 ppm; where ch and c0, are the sound speed in humid and in dry air, respectively. Comparisons are made with known experimental measurements and theoretical data.

The reverberation technique of Knudsen has been applied to the measurement of the absorption of sound over the frequencies 300 to 3000 cps in air with mole ratio concentrations of water vapor ranging from 0 to 0.02. Pressures from 5 cm Hg to atmospheric and temperatures from 0°C to 65°C were employed in the study. With the use of a 66-in. spherical resonator and dry nitrogen gas as reference, following the method of Delsasso and Leonard, it has been possible to observe the anomalous absorption of humid air down to 300 cps. Pertinent graphs for the gases studied and detailed description of the experimental apparatus will be presented. [Support of this work by subcontract with the University of Michigan Signal Corps Contract No. DA-36-039-SC-52654 is acknowledged.]