Robert W. Young

Terminology for Logarithmic Frequency Units

Fletcher has proposed the use of a logarithmic frequency scale such that the frequency level equals the number of octaves, tones, or semitones that a given frequency lies above a reference frequency of 16.35 cycles/sec., a frequency which is in the neighborhood of that producing the lowest pitch audible to the average ear. The merits of such a scale are here briefly discussed, and arguments are presented in favor of this choice of reference frequency. Using frequency level as a count of octaves or semitones from the reference C0, a rational system of subscript notation follows logically for the designation of musical tones without the aid of staff notation. In addition to certain conveniences such as uniformity of characters and simplicity of subscripts (the eight Cs of the piano, for example, are represented by C1 to C8) this method shows by a glance at the subscript the frequency level of a given tone counted in octaves from the reference C0 = 16.352 cycles/sec. From middle C4, frequency 261.63 cycles/...

Inharmonicity of Plain Wire Piano Strings

The inharmonicity of plain wire strings in situ has been measured in six pianos of various styles and makes. By inharmonicity is meant the departure in frequency from the harmonic modes of vibration expected of an ideal flexible string. It is shown from the theory of stiff strings that the basic inharmonicity cents (hundredths of a semitone) is given by 3.4×1013n2d2/v02l4, where n is the mode number, d is the diameter of the wire in cm, l is the vibrating length in cm, and v0 is the fundamental frequency. A value of Q/ρ = 25.5 × 1010 (cm/sec)2 was assumed for the steel wire, where Q is Youngs modulus and ρ is the density. The observations are entirely compatible with the relationship given. In general terms the inharmonicity of the plain steel strings is about the same in all the pianos tested, being about 1.2 cents for the second mode of vibration of the middle C string. Above this point every eight semitones it is doubled. Below middle C the inharmonicity is consistently less in large pianos than in sm...

On the Energy Transported with a Sound Pulse

Definitions of Fourier pressure spectrum level and integrated band pressure level are proposed for engineering description of the spectra of sonic booms and explosive sounds, and relations to specific energy spectral density are demonstrated.

Re‐Vision of the Speech‐Privacy Calculation

The articulation index used in telephone communication, the listening equation for SONAR, and the acoustical privacy calculation of architectural acoustics are all founded on a computation of an excess of signal level over noise level just sufficient to permit some stated detectability. From this viewpoint, data compiled for “Speech Privacy in Buildings” [Cavenaugh, Farrell, Hirtle, and Watters, J. Acoust. Soc. Am. 34, 475–492 (1962)] have been reviewed for possible simplications in their procedure for estimating acoustical privacy. In lieu of the “dot counting” method, ratings of sound isolation here investigated include the sound transmission class (STC), a similar index being discussed for international standardization (IISO), and a frequency‐weighted sound isolation; as measures of ambient noise, in lieu of curves to be fitted for different spectrum shapes, sound level (A) and frequency‐weighted octave‐band sound‐pressure levels have been tested. The reported judgments of be correlated at least as wel...

Single‐Number Criteria for Room Noise

Subjective noise ratings by executive office personnel, reported at the time that the NC curves were introduced [L. L. Beranek, J. Acoust. Soc. Am. 28, 833–852 (1956)], have been correlated with various physical measures derived from the 17 noise spectra originally published. The rank‐order correlation coefficients (in parentheses) for the respective physical measures are: A‐sound level (0.96), B‐sound level (0.96), NC level (0.95), NCA level (0.95), N level per ISO proposal (0.96), speech‐interference level (0.86), speech‐interference level based on the three octave‐band levels from 300 to 2400 cps (0.91), calculated loudness level (0.96), perceived‐noise level (0.96), 40‐noy‐weighted sound level (0.95). With only one exception each, loudness level and perceived‐noise level for the 17 airbase office noises are 13±1 dB greater than the A‐sound level. Some type noise spectra of various shapes are provided, along with an auxiliary table, to facilitate estimation of the several physical measures simply by cu...

Image Interference in the Presence of Refraction

Underwater sound transmission has been studied as a function of range at frequencies of 0.2, 0.6, 1.8, 7.5, and 22.5 kc, under a variety of thermal conditions. At the three lower frequencies, marked interference patterns are observed. These result from the combination of surface reflected sound (as from an image source) and directly transmitted sound. Refraction modifies the interference pattern. When the sound velocity increases with increasing depth, the interference pattern is contracted; when the velocity increases with depth, the pattern is extended. An easily used formula is developed to predict this influence of refraction on the propagation of sound emitted from a point source adjacent to a reflecting plane. The theory is in good agreement with the experimental data obtained with the source at a depth of 14 feet from the surface and the receiver as deep as 300 feet.

Penetration of Sonic Booms into the Ocean

Underwater sound pressures have been measured in comparison with sound pressures in air resulting from sonic booms generated by aircraft flying near Mach 1.1. Microphones typically were mounted 1 and 12 ft (on the average) above the perturbed ocean surface, and displaced laterally at least 1000 ft; hydrophones were suspended 20, 80, and 160 ft below the surface. Sound‐pressure waveforms from the two microphones, passed by octave‐band filters in the lower audio‐frequency range, were of comparable amplitude and approximately 10 times greater in amplitude than those from the shallow hydrophone; the waveforms were very different, however, from air and from water. In order to characterize a total pulse, the squared sound pressure within the octave was integrated in time. The resulting octave‐band, pressure‐squared‐time levels from the two microphones agreed with each other for a given flyover and constituted a spectrum sloping downward about 4 dB/oct; the corresponding spectra from the hydrophones tended to ex...

Dependence of Tuning of Wind Instruments on Temperature

Observations by Pottle on the change of tuning of musical wind instruments with ambient temperature are here summarized by a single coefficient representing each instrument tested. The largest effect was observed on the BB♭ sousaphone where the increase with ambient temperature occurred at the rate of 2.6 cents/°C. This is equivalent to a fractional frequency coefficient of 1.6 × 10−3/°C. The cent is a logarithmic unit of frequency ratio such that 1200 cents equals one octave. A theory is developed by which the average temperature (and thus the velocity of sound) of the air within a wind instrument may be inferred from the empirically determined dependence of equilibrium tuning on ambient temperature. The theory also provides a qualitative estimate of the change in tuning which occurs while the instrument is first being warmed by the players breath.

Sound Pressure in Water from Source in Air

Sound pressure in the water under a point source overhead in air is shown by theory and experiment to propagate as from a virtual source situated (c1/c2) times the actual source height above the water and emitting unit‐distance sound pressure that is (2c1/c2) times the actual unit‐distance sound pressure, where c1 and c2 are the speeds of sound in air and water, respectively.

Reference Pressure for Sound‐Pressure Level

Dissatisfaction with 0.0002 μbar as a reference pressure for sound‐pressure level is not really widespread; a broad view of the benefit to be derived from general use of a single small reference pressure has led to proposed standardization on 0.0002 μbar for all media.