Martin Greenspan

Tables of the Speed of Sound in Water

An equation and tables for the speed of sound in water are reprinted from a recent paper published in The Journal of Research of the National Bureau of Standards.

Piston radiator: Some extensions of the theory

Those results of the theory of the baffled, uniform‐piston radiator that can be calculated exactly are extended to some other cases, especially the simplest case of a simply supported radiator, the simplest case of a clamped‐edge radiator and a Gaussian radiator. It is also shown that from the solution to a problem with boundary conditions framed in terms of velocity, the solution to a corresponding problem, having boundary conditons framed in terms of pressure, can be obtained very easily.

Gas‐filled spherical resonators: Theory and experiment

Gas‐filled spherical resonators are excellent tools for routine measurement of thermophysical properties. The radially symmetric gas resonances are nondegenerate and have high Q’s (typically 2000–10 000). Thus they can be used with very simple instrumentation to measure the speed of sound in a gas with an accuracy of 0.02%. We have made a detailed study of a prototype resonator filled with argon (0.1–1.0 MPa) at 300 K, with the objective of discovering those phenomena which must be understood to use gas‐filled spherical resonators to measure the thermodynamic temperature and the universal gas constant R. The resonance frequencies fN and half‐widths gN were measured for nine radially symmetric modes and nine triply‐degenerate nonradial modes with a precision near 10−7 fN. The data were used to develop and test theoretical models for this geometrically simple oscillating system. The basic model treats the following phenomena exactly for the case of a geometrically perfect sphere: (1) the thermal boundary la...

Propagation of Sound in Five Monatomic Gases

The speed and attenuation of sound at 11 Mc were measured in He, Ne, A, Kr, and Xe at various pressures between atmospheric and a few mm Hg, and the results were compared with existing theories.

Acoustic emission: some applications of Lamb’s problem

A method for obtaining the signatures (waveforms) of certain acoustic emission events has been developed. The waveform is that at the source, free of contamination by ringing of the specimen, apparatus, and transducer. The technique is based on the comparison of two signals at the transducer, one from the event in question and one from an artificial event of known waveform. The apparatus is also adapted to the calibration of transducers in a certain sense. The configurations of source (real or simulated acoustic−emission event) and receiving transducer correspond to those of some special cases of Lamb’s problem. As a byproduct, the results may be of some interest to seismologists.Subject Classification: 40.42; 35.54, 35.80, 35.68; 40.50; 85.44.

Rotational Relaxation in Nitrogen, Oxygen, and Air

The speed and attenuation of sound at 11 Mc were measured in N2, O2, and dry air at various pressures between atmospheric and a few mm Hg. The rotational collision numbers were found to be: for N2, 5.26±0.05; for O2, 4.09±0.08; for air, 4.82±0.18.

The NBS conical transducer: Analysis

The NBS conical transducer is a sensitive, broadband device for the measurement of surface displacement as a function of time. Its uses include acoustic‐emission testing. Here, the operation of this transducer is subjected to a straightforward analysis. Although several approximations, some more dubious than others, are made, the model predicts the main features rather well. The important parameters are the size and shape of the active element, the source impedance (looking into the area whose deflection is being measured), and the terminating impedance (back load).

Surface‐wave displacement: Absolute measurements using a capacitive transducer

We have constructed a capacitive transducer for the absolute measurement of the normal component of surface‐wave motion on a flat solid, the direction of travel of the wave being known. The transducer backplate is a cylinder and has cylindrical extensions on each end that act as electrostatic guards to render calculable the sensitivity and capacitance of the transducer. Compliant support elements are incorporated, resulting in negligible mechanical loading to the surface and flat frequency response over the range of 10 kHz to 1 MHz or better. The amplifier noise floor is equivalent to about 4×10−12 m rms with a 5‐MHz bandwidth. The upper limit to displacements measurable by this technique has not been established, but is large enough to encompass the range of interest. Estimated uncertainty of the sensitivity determination is less than 5%.

Ultrasonic‐transducer power output by modulated radiation pressure

We have set up and are using an apparatus for the measurement of total sound power output of a piezoelectric transducer radiating into water. This apparatus combines the better features of previously used methods which depend on radiation pressure. The input is modulated at a low frequency and the output power is intercepted by a target which experiences a force at the modulation frequency. The target is mounted on the armature of an electromagnetic receiver provided with an independent coil through which a current at the modulation frequency is adjusted in amplitude and phase, either manually or automatically by feedback, to arrest the motion of the armature. When the armature is stationary the force depends only on the current, and the apparatus can be calibrated using direct current and dead weights. It is thus absolute. In practice, the carrier frequency is swept over any part of the range 0.1–15 MHz while a recording of power output versus frequency is made. The results of comparisons made with those of other mehtods are encouraging. Examples of curves from normal and defective transducers are shown.

Combined Translational and Relaxational Dispersion of Sound in Gases

It is shown that for a special value of the Prandtl number the Stokes‐Kirchhoff equation governing the propagation of sound in a fluid is factorizable even for complex values of the heat conductivity and specific heats. A solution allowing for the dispersion due to both translational and thermal relaxation is thus obtained in simple form for this special case which, however, is representative of many gases with considerable accuracy.