A recent survey of piano acoustics literature revealed an apparent lack of attention to various aspects of dispersion in piano strings, apart from some information on its effect on inharmonicity of piano tone partials. In this article, it will be shown how group velocity of transverse waves in piano strings can be measured as a function of frequency with the aid of a short-time spectral analysis method. Examples of group velocity measurements appear to be essentially in agreement with the theoretical predictions based on a model of a flexurally stiff string. In addition, the relationship between the group and phase velocity, as a function of frequency, is also illustrated, indicating correspondence between theoretical predictions and experimental results. A short-time spectral analysis of transverse string displacement as a function of time, monitored near the bridge, has revealed a quasiperiodic succession of frequency glides. This effect is due to dispersion and is particularly prominent in the lowest bass strings. However, the same type of analysis applied to the sound-pressure signal of the corresponding radiated sound yielded somewhat different results. While frequency glides similar to those found in the string displacement spectra were partly evident in the sound-pressure spectra, strong precursive components of longitudinal string vibration origin were found to dominate the higher frequency portion of the attack transient of the radiated sound.
Translational energy spectra have been obtained for single-electron capture by 8 keV Ar4+ ions in He, Ne and Ar. The spectra for He and Ne targets display eight well-resolved peaks, the majority of which correspond to capture involving a rearrangement of the electron core configuration. By contrast, the five channels observed in the spectrum for the Ar target are all associated with core-conserved electron-capture processes. One pronounced peak in the spectra for He and Ne cannot be explained on the basis of capture from the ground 'P or metastable 'D and 'S states of the Ar4+ ions, and appears to originate from capture by Ar4+ in the hitherto unidentified metastable %'-state at -7.5 eV above the ground state. All observed channels are spin-conserved.Charge-transfer processes involving multiply charged ions play an important role in diverse fields of physics, including thermonuclear fusion and astrophysical research, as well as in the design of XUV lasers. Translational energy spectroscopy is an invaluable tool in helping to identify state-selective channels, crucial for the proper understanding of curve-crossing mechanisms and plasma diagnostics. Unambiguous identification of the relevant reaction channels is often complicated by the presence of metastable states in the primary ion beam, and by the multiplicity and closeness of energy-separation of the prospective exit channels. This is exemplified by capture into high excited states of the product incident ion, as in the case of capture by Ar4+ in Ar, but guided by spin consideration^,'-^ our relatively unclustered spectrum is more amenable to confident identification than expected.There is a paucity of translational energy data for single-electron capture by Ar4+ ions, but capture by Ar4+ in He is included in a recent study by McCullough et a1.4 on state-selective capture by Ar4+, A?+ and Arb+ in H , H, and He, and in a general study on the translational energy spectroscopy of Arq+ (q = 1 to 4) ions carried out in this laboratory (see Hamdan et d 5 ) . In our present investigation, we have obtained high resolution spectra for single-electron capture by 8 keV Ar4+ in He, Ne and Ar. We are not aware of other existing high-resolution data for Ne and Ar targets.The Ar4+ ion has a 3P ground-state, and low-lying metastable singlet 'D and 'S states which are known5 to populate the incident ion beam in our collision region. All these states participate in electron-capture processes. The Ar3+ ion has a doublet-quartet system. Accordingly, all capture channels for Ar4+ + Ar3+ originating from the 3P-state of Ar4+ are spin-conserved, whereas only the doublet-states of Ar3+ are accessible from electron capture by the metastable singlet 'D and 'S states of Ar4+ if spin-conservation is strictly observed. All identified capture channels in our three spectra conform to this requirement.There are seven well-defined capture channels observed in each of the spectra for Ar4+ in He and Ne involving capture from the 3P, 'D and 'S states of Ar4+. Six of these transitions result in a...
The percussive excitation of a piano string by a hammer is expected to produce longitudinal string vibration components in addition to the desired transverse ones [e.g., Yanagisawa et al., J. Acoust. Soc. Jpn. 33, 412–416 (1977)]. However, so far little quantitative information exists in current acoustics literature on the contribution of such longitudinal components to the radiated sound of a piano. Our investigations revealed the presence of intial components of radiated sound generated by the longitudinal string vibration mechanism. These components, coined as the precursive sound, appear distinctly ahead of the main body of sound that is almost entirely due to transverse string vibration. Our experimental data on the longitudinal modes in piano strings indicate that the most apparent contribution to the radiated sound occurs in the attack transient of tones in the low bass register. For the lowest bass tones, the sound-pressure level (SPL) of the precursive sound may be only 10 to 20 dB below the overall peak SPL and the decay rate of the order of 100 dB/s. [Work supported by A.R.G.S. and C.T.E.C.]
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