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On the acoustics of tuning forks
Abstract
Tuning forks can vibrate in many different modes in which the tines move
either in the plane or perpendicular to the plane of the fork.
Symmetrical modes can be modeled by the motion of two cantilever beams,
antisymmetrical modes by the motion of a beam with free ends. A tuning
fork vibrating in its fundamental mode is approximately a linear
quadrupole sound source whose strength can be increased by use of a
baffle or by touching the stem to a soundboard. The motion of the stem
includes strong components at both the fundamental frequency and its
second harmonic. Slight alterations in a tuning fork can enhance or
suppress either of these components. At large amplitudes, the tines
vibrate nonsinusoidally, the nth harmonic increasing approximately as
the nth power of the fundamental.
... This is known as the X-cut seen in Figure 6 and it vibrates in the xy-plane. The tuning fork frequency of vibration of the first harmonic, [21,43,44]. ...
The technological discoveries and developments since dawn of civilization that resulted in the modern wristwatch are linked to the evolution of Science itself. A history of over 6000 years filled with amazing technical prowess since the emergence of the first cities in Mesopotamia established by the \v{S}umer civilization. Usage of gears for timekeeping has its origin in the Islamic Golden Age about 1000 years ago. Although gears have been known for over 2000 years such as found in the Antikythera Mechanism. Only in the seventeenth century springs started to be used in clock making. In the eighteenth century the amazing \textit{Tourbillon} was designed and built to increase clock accuracy. In the nineteenth century the tuning fork was used for the first time as timebase. Wristwatches started to become popular in the beginning of the twentieth century. Later in the second half of the twentieth century the first electronic wristwatch was designed and produced, which brings us to the curious case of the Bulova \textit{ACCUTRON} caliber 214 the first transistorized wristwatch, another marvel of technological innovation and craftsmanship whose operation is frequently misunderstood. In this paper the historical evolution of timekeeping is presented. The goal is to show the early connection between Science and Engineering in the development of timekeeping devices. This linked development only became common along the twentieth century and beyond.
... This is known as the X-cut seen in Figure 6 and it vibrates in the xy-plane. The tuning fork frequency of vibration of the first harmonic, 21,43,44 . ...
The technological discoveries and developments since dawn of civilization that resulted in the modern wristwatch are linked to the evolution of Science itself. A history of over 6000 years filled with amazing technical prowess since the emergence of the first cities in Mesopotamia established by the \v{S}umer civilization. Usage of gears for timekeeping has its origin in the Islamic Golden Age about 1000 years ago. Although gears have been known for over 2000 years such as found in the Antikythera Mechanism. Only in the seventeenth century springs started to be used in clock making. In the eighteenth century the amazing \textit{Tourbillon} was designed and built to increase clock accuracy. In the nineteenth century the tuning fork was used for the first time as timebase. Wristwatches started to become popular in the beginning of the twentieth century. Later in the second half of the twentieth century the first electronic wristwatch was designed and produced, which brings us to the curious case of the Bulova \textit{ACCUTRON} caliber 214 the first transistorized wristwatch, another marvel of technological innovation and craftsmanship whose operation is frequently misunderstood. In this paper the historical evolution of timekeeping is presented. The goal is to show the early connection between Science and Engineering in the development of timekeeping devices. This linked development only became common along the twentieth century and beyond.
... The resulting vibration amplitudes varied between trials ( Fig 1B). This aligns with a previous finding that tuning fork vibration waveforms are sensitive to the strength of the blow used to generate the vibrations [5]. We also found that the 128 Hz tuning fork resonated at 178 Hz instead of 128 Hz (Fig 1C). ...
Traditionally, clinicians use tuning forks as a binary measure to assess vibrotactile sensory perception. This approach has low measurement resolution, and the vibrations are highly variable. Therefore, we propose using vibrations from a smartphone to deliver a consistent and precise sensory test. First, we demonstrate that a smartphone has more consistent vibrations compared to a tuning fork. Then we develop an app and conduct a validation study to show that the smartphone can precisely measure a user's absolute threshold. This finding motivates future work to use smartphones to assess vibrotactile perception, allowing for increased monitoring and widespread accessibility.
Regarding a tuning fork, which is often used in science education, what kind of sound field is formed around it is not fully understood. Under these circumstances, we attempted a visualization of the sound field formed around a tuning fork using Improved-FDM for calculation of elastic wave propagation. As a result, visualization images of sound waves and amplitude distribution around tuning forks were obtained. From the images, the sound field characteristics of the tuning fork were confirmed to have four maxima at short distances and two maxima at long distances around the forks. In addition, it was shown that the characteristics of the sound field around the tuning fork are easy to understand if they are interpreted based on the sound field around the single sound source.
Nitrogen-vacancy (NV) center in diamond is a promising quantum sensor with remarkably versatile sensing capabilities. While scanning NV magnetometry is well-established, NV electrometry has been so far limited to bulk diamonds. Here we demonstrate imaging external alternating (AC) and direct (DC) electric fields with a single NV at the apex of a diamond scanning tip under ambient conditions. A strong electric field screening effect is observed at low frequencies. We quantitatively measure its frequency dependence and overcome this screening by mechanically oscillating the tip for imaging DC fields. Our scanning NV electrometry achieved an AC E-field sensitivity of 26 mV μm ⁻¹ Hz −1/2 , a DC E-field gradient sensitivity of 2 V μm ⁻² Hz −1/2 , and sub-100 nm resolution limited by the NV-sample distance. Our work represents an important step toward building a scanning-probe-based multimodal quantum sensing platform.
Tuning fork experiments at the undergraduate level usually only demonstrate a tuning fork's linear resonance. In this paper, we introduce an experiment that can be used to measure the nonlinear frequency response curve of a regular tuning fork. Using double-grating Doppler interferometry, we achieve measurement precision of the oscillation amplitude in the range of microns. With this experimental setup, we observe nonlinear behaviors of the tuning fork, such as the softening frequency response curve and the jump phenomenon. This provides an integrated experiment for intermediate-level students and a basis for senior research projects.
This paper describes ongoing developments to an advanced laboratory course at Kettering University, which is targeted to students in engineering and engineering physics and emphasizes theoretical, computational, and experimental components in the context of airborne acoustics and modal testing [cf. D. A. Russell and D. O. Ludwigsen, J. Acoust. Soc. Am. 131, 2515–2524 (2012)]. These developments have included a transition to electronic laboratory notebooks and cloud-based computing resources, incorporation of updated hardware and software, and creation and testing of a multiple-choice assessment instrument for the course. When Kettering University suddenly shifted to exclusively remote teaching in March 2020 due to the COVID-19 pandemic, many of these changes proved to be essential for enabling rapid adaptation to a situation in which a laboratory was not available for the course. Laboratory activities were rewritten by crowdsourcing archived data, videos were incorporated to illustrate dynamic phenomena, and computer simulations were used to retain student interactivity. The comparison of multiple measures, including the assessment instrument, team-based grades on project papers, and individual grades on final exams, indicates that most students were successful at learning the course material and adapting to work on team-based projects in the midst of challenging remote learning conditions.
Soft tactile sensor design is commonly implemented with
conductive, stretchable materials that are either soft themselves or
embedded in an elastomeric matrix. It is well documented that embedded
3D printing (e-3D) overcomes the limitations of these processes, such as
delicate hard-soft interfaces, poor shape fidelity, intricate manufacturing
processes, and extensive multi-step casting. This paper proposes a precise and accessible e-3D setup by combining a cost-effective fused deposition modeling (FDM) printer with a high-precision extruder suitable
for soft materials and liquids. We designed and fabricated four sensor
patterns that were evaluated in stretch and normal force experiments.
The results indicate, that the three sensors under normal force were able
to detect qualitative contact changes, while the one exposed to stretch
performed similar to previous work in the literature. These preliminary
results prove the feasibility of the proposed setup, which will be used
as an optimization and evaluation platform for future soft tactile sensor
development
Haptic feedback is envisioned to be a powerful tool in (digital) orthosis fitment procedures. In context of a larger research project on digital molding and developing a glove for orthopedic experts, we explored the use of vibrotactile feedback on the wrist for wrist angle adjustments. Five different patterns are presented on both the inside and outside of the wrist as well as crossing signals. Participants were asked to indicate whether the pattern was communicating that the wrist angle had to be increased or decreased by moving the hand up or down. The results show that the vibrotactile stimuli are being interpreted consistently by the participants, provided the patterns are presented on one side of the arm. Although the interpretations were consistent within participants, there were individual differences in the reported directions of the signals, which makes it important to take into account personal preferences and calibration when implementing haptic feedback.
Prior research has shown that the direction of a user’s focus affects the perception of tactile cues. Additionally, user agency over touch stimulation has been shown to affect tactile perception. With the development of more complicated haptic and multi-sensory devices, simple tactile cues are rarely used in isolation and the effect of focus direction and of user agency on the perception of a sequence of tactile cues is unknown. In this study, we investigate the effect of both of these variables, focus direction and agency, on the perception of a cue sequence. We found that the direction of user focus and user sense of agency over tactile stimulation both had a significant effect on the accurate perception of a cue sequence. These results are presented in consideration for developing better haptic devices that account for users’ focus on and control over these devices.
Compressional, torsional, and bending waves in bars and plates can be studied with simple apparatus in the laboratory. Although compressional and torsional waves show little or no dispersion, bending waves propagate at a speed proportional to (f)1/2. Reflections at boundaries lead to standing waves that determine the vibrational mode shapes and mode frequencies. Boundary conditions include free edges, simply supported edges, and clamped edges. Typical mode shapes and mode frequencies for rectangular bars, circular plates, and square plates are described.
The sounds from certain types of gongs show a frequency shift, up or down, as the vibration decays. In order to understand this nonlinear behavior, we have studied the vibrations of a variety of flat and curved plates under varying amounts of radial tension or compression. Flat plates show a nonlinearity of a hardening type (falling frequency), whereas most curved plates show softening behavior (rising frequency). The degree of the nonlinearity appears to be sufficient to explain the observed frequency shift in the gongs studied.