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The case of symmetric vibrations of a circular membrane fixed at its rim has many applications, so this situation holds great interest for us. Vibrational symmetry implies a solution to the wave equation (6.4) that is independent of $\theta$ , and we limit the solutions for this case to
$$z_{0n} = A_{0n} J_0(k_{0n} ... | {
"Header 1": "6.5 Case Study: Symmetric Vibrations of a Circular Membrane Fixed at its Perimeter",
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Modifying Equation (6.3) to include this incremental force we obtain
$$\nabla^2 z - \frac{1}{c^2} \frac{\gamma P_0}{\rho_0 V_0} \pi a^2 \langle z \rangle = \frac{1}{c^2} \frac{\partial^2 z}{\partial t^2}$$
(6.28)
The term $\langle z \rangle$ is an integral function of all the permitted modes of vibration, which m... | {
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The average displacement $\langle z \rangle_s$ of the driven membrane is found by averaging over the surface area of the membrane:
$$\langle z \rangle_{s} = \frac{2\pi e^{i\omega t} \int_{0}^{a} \frac{P}{k^{2}T} \left[ \frac{J_{0}(kr)}{J_{0}(ka)} - 1 \right] r \, dr}{\pi a^{2}}$$
$$= \frac{P}{k^{2}T} \frac{J_{2... | {
"Header 1": "6.5 Case Study: Symmetric Vibrations of a Circular Membrane Fixed at its Perimeter",
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The term $J_0(iKr)$ is a modified Bessel function of the first kind, generally written as
$$\frac{d^2y}{dx^2} + \frac{1}{x}\frac{dy}{dx} - \left(1 + \frac{n^2}{x^2}\right)y = 0$$
<sup>&</sup>lt;sup>2</sup> The modified Bessel functions $I_n(x)$ are solutions of the modified Bessel differential equation
$I_0(K... | {
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Prove that the total energy of a circular membrane vibrating in its fundamental mode is equal to 0.135πρ*s*(*a*ω*A <sup>f</sup>* ) <sup>2</sup> where ρ*<sup>s</sup>* is the area density, *a* the radius of the membrane, and ω the angular frequency of the vibration, and *A <sup>f</sup>* the fundamental amplitude at the c... | {
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#### 7.1 Introduction
In dealing with strings, bars, and membranes in Chapters 4–6, we considered relatively simple geometric conditions. The situation becomes more complex when the sound waves are confined in a restricted amount of space. For example, when sound propagates inside a rigid-walled pipe with a wavelengt... | {
"Header 1": "7 Pipes, Waveguides, and Resonators",
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#### 7.4 The Open-Ended Pipe
Consider a pipe driven at x = 0 but open-ended at the other end x = L. The assumption that $\mathbf{Z}_{nL} = 0$ at x = L (which would lead to resonances at $f_n = \frac{1}{2} nc/L$ ) is not valid, because the open end of the pipe radiates into the surrounding air. The appropriate co... | {
"Header 1": "7 Pipes, Waveguides, and Resonators",
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According to Equation (7.25) the nodes are located at
$$k(L - x_n) - \frac{\theta}{2} = \left(n - \frac{1}{2}\right)\pi$$
(7.27)
For the first node (n = 1),
$$\theta = 2k(L - x_1) - \pi \tag{7.28}$$
#### Example Problem 1
An impedance tube is found to have a SWR of 3 and the first node is 3/8 of the wavelengt... | {
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with permitted values of $k_{xl}$ and $k_{ym}$ , resulting from the boundary conditions of rigidity, these being
$$k_{xl} = \frac{l\pi}{L_x},$$
$l = 0, 1, 2, ...$
$k_{ym} = \frac{m\pi}{L_y},$ $m = 0, 1, 2, ...$ (7.40)
We rearrange Equation (7.39) to find $k_z$
$$k_z = \sqrt{\frac{\omega^2}{c^2} - k_{xl}^... | {
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An impedance match must be made at the waveguide entry z=0 so that the permissible mode solutions comply with the acoustic behavior of the active surface. If we know the pressure or velocity distribution of the driving source, these can be correlated with the behavior of $\mathbf{p}(x, y, 0, t)$ for the pressure or ... | {
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Then inserting the solution into Equation (7.62) results in
$$(-\mathbf{B}\omega^2 m + i\mathbf{B}\omega R_r + \mathbf{B}S)e^{i\omega t} = APe^{i\omega t}$$
Solving for **B** provides the following complex displacement:
$$\delta = \frac{APe^{i\omega t}}{i\omega \left[R_r + i\left(m\omega - \frac{S}{\omega}\right)... | {
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A 70 dB (re 20 $\mu$ Pa) 1 kHz signal is incident normally to a boundary between the air and another medium having a characteristic impedance of 780 Pa s/m.
- (a) Determine the effective root-mean-square pressure amplitude of the reflected waves.
- (b) Determine the effective root-mean-square pressure of the transmitt... | {
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#### 8.1 Introduction
In this chapter we deal with lumped and distributed acoustic elements, applying electrical and mechanical analogs to acoustic behavior in order to treat different duct geometries, acoustic filters, and networks. The reflection and transmission of sound waves at piping interfaces, where the acous... | {
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"Header 2": "Acoustic Analogs, Ducts, and Filters",
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#### 8.4 Waves in Pipes: Junctions and Branches
Consider a sound wave traveling in the positive x-direction, represented by
$$\mathbf{p}_i = \mathbf{a}e^{i(\omega t - kx)},\tag{8.9}$$
is incident upon a point x = 0, where the acoustic impedance changes from $\rho_0 c/A$ to some complex value $\mathbb{Z}_0$ .... | {
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"Header 2": "Acoustic Analogs, Ducts, and Filters",
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The reflection and transmission coefficients become
$$R_p = \left|\frac{\mathbf{b}}{\mathbf{a}}\right|^2 \frac{\left(\frac{\rho_0 c}{2A}\right)^2}{\left(\frac{\rho_0 c}{2A} + R_g\right)^2 + X_g^2}$$
(8.23)
$$T_{p} = \left| \frac{\mathbf{a}_{t}}{\mathbf{a}} \right|^{2} = \frac{R_{g}^{2} + X_{g}^{2}}{\left( \frac{\rh... | {
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As a rule, a number of orifices strategically placed apart can attenuate at low frequencies more effectively than a single orifice of equal total area.
The sound power transmission coefficient *Tpg* into a single orifice is approximated by
$$T_{pg=} \frac{2k^2 A}{\pi \left[ \left( \frac{2AkL'}{\pi a^2} \right)^2 + ... | {
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"Header 2": "Acoustic Analogs, Ducts, and Filters",
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A duct system can be modeled as a source-path-termination model with a source load, as shown in Figure 8.12. These models are interrelated when the path-termination is treated as a load. This type of model is commonly used, say, for engine-exhaust-pipe-tailpipe-radiation system. Referring to Figure 8.13, the three mo... | {
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"Header 2": "Acoustic Analogs, Ducts, and Filters",
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The main pipe is transmitting plane waves with frequencies such that their wavelengths are much larger than the diameter of either pipe.
- (a) Develop an equation for the transmission coefficient in the main pipe.
- (b) Do the same thing for the branch pipe.
- (c) Let the area of the main pipe be twice as much as that ... | {
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#### 9.1 Introduction
Acoustic measurements constitute an essential step in order to establish the status of an acoustic environment and to develop a systematic approach toward modifying the environment and to set up criteria for improvements. Other more recently developed methodologies of acoustical measurements ent... | {
"Header 1": "9",
"Header 2": "Sound-Measuring Instrumentation",
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#### Solution
Equation (9.3) is applied to yield
$$E_{\text{out}} = 2 \times 10^{-4} \times 10^{(85-50)/20} \text{ V} = 0.0112 \text{ V} = 11.2 \text{ mV}$$
Microphone sensitivities typically range between 0.5 $\mu$ V/ $\mu$ bar (-125 dB V/ $\mu$ bar) and 3 mV/ $\mu$ bar (-50 dB V/ $\mu$ bar). A microphone use... | {
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"Header 2": "Sound-Measuring Instrumentation",
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The microphone spacing should be considerably smaller than the wavelength of the sound being measured in order to yield valid results from two-point measurements. For example, in order to sustain an accuracy of $\pm 1$ dB, the upper frequency limit for 1-cm microphones set apart 12 mm from each other is approximately... | {
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If we consider a 2-s burst of sound at the rms pressure of 1 Pa, use of Equation (9.6) will indicate an SEL of 97 dB. Comparison of Equations (9.5) and (9.6) leads to the relationship between SEL and *L*eq:
$$SEL = L_{eq} + 10 \log T \tag{9.7}$$
#### *Example Problem 3*
What is the SEL for an equivalent sound lev... | {
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A valuable means of analyzing noise is the evaluation of sound in each frequency band. If a machine emits a noise that indicates it is malfunctioning, the analysis of the sound output according to frequency can provide vital clues as to which component of the machine is defective. This situation calls for the use of a ... | {
"Header 1": "9.11 Noise Measurement in Selected Frequency Bands, Band Pass Filters",
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The FFT analyzer captures a block of sampled data of finite length (generally 1024 or 2048 samples) for a processing interval. In transforming from the time domain to the frequency domain, the Fourier transform relates a function of time g(t) to a function of frequency $F(\omega)$ in the following manner:
$$F(\omeg... | {
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#### 9.15 Resolution
The smallest increment in a parameter that can be displayed by a measurement system is the *resolution* for that system. In FTT analysis, the resolution is expressed by
$$\beta = \frac{f_s N}{N} = \frac{2f_R}{N} \tag{9.18}$$
FIGURE 9.20. Typical weighting func... | {
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We can summarize the measurement procedure in a free field over a reflecting plane as follows:
- 1. The source is surrounded with an imaginary surface of area *S*, either a hemisphere of radius *r* or a rectangular parallelepiped.
- 2. The area of the hypothetical surface is calculated. $S = 2\pi r^2$ in the case o... | {
"Header 1": "9.18 Measurement of Sound in a Free Field over a Reflecting Plane (Semianechoic Chamber)",
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The relationship between the sound power of a source and the average reverberant sound level can be determined and allows calculation of the sound power.
The procedure for measuring the sound power level in an echoic chamber may be summarized as follows:
1. The reverberation time $T_{60}$ is measured by using a s... | {
"Header 1": "9.18 Measurement of Sound in a Free Field over a Reflecting Plane (Semianechoic Chamber)",
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In testing the performance of a loudspeaker through traditional analog means, a sine wave generator provides a signal to the loudspeaker and a calibrated microphone picks up the loudspeaker's acoustical output and feeds it to a spectrum analyzer, which then relays the data to a display or a recorder. The dedicated func... | {
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#### 10.1 Human Hearing
The mechanism of the human ear has been a source of much wonder for physiologists, who are progressing well beyond the fragmentary knowledge of the past by continually uncovering layers of new marvels of how the human ear really functions. Our hearing mechanism is a complex system that consist... | {
"Header 1": "10 Physiology of Hearing and Psychoacoustics",
"token_count": 1998,
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The *inner hair cells* are arranged in a single row on the modiolar side of the tunnel of Corti, and the *outer hair cells* exist in three parallel rows on the strial side of the tunnel of Corti. The inner hair cells are round and squat; their upper surfaces contain about 50–70 hairs called *stereocilia*. The outer hai... | {
"Header 1": "10 Physiology of Hearing and Psychoacoustics",
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Most people with age-induced or noise-induced hearing impairment first lose hearing acuity at high frequencies, making it difficult for them to distinguish consonants, especially *s* versus *f* , and *t* versus *z*. Such persons must strain harder to understand conversations. Going to the movies, listening to lectures,... | {
"Header 1": "10 Physiology of Hearing and Psychoacoustics",
"token_count": 1911,
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|
| Frequency,<br>Hz or kHz | Mean SPL, dB | $\sigma$ , dB | SPL at $2\sigma$ below mean | ANSI, 1969 |
|-------------------------|--------------|---------------|-----------------------------|------------|
| | · | <u> </u> ... | {
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Even over the telephone, individual voices are recognizable because of the differences in their sound spectra.
#### *Masking*
*Masking* is said to have occurred when the audibility of a sound is interfered with by the presence of noise or other background sound. The "cocktail party" effect, which makes it difficult... | {
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Calculation for the Articulation Index in the Sample Problem.
#### *Example Problem 1: Calculation of AI*
Let us compute the articulation index of a male voice speaking at a normal level 1 m from the listener in the presence of pink noise that contributes 47 dB in each octave band.
#### *Solution*
Table 10.4 is... | {
"Header 1": "10 Physiology of Hearing and Psychoacoustics",
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Algorithms also manage noise: owing to the fact that speech sound intensities can change radically in a millisecond whereas noise is more acoustically stable over a comparatively longer time. On a time basis, DSP can reduce the levels of continuous sounds such as traffic noise and household appliances. And it simultane... | {
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They are also studying animals that have been deafened by other means, older animals and animals that have been deaf for longer periods of time before treatment begins. If these experiments turn out to be successful, the studies necessary to ensure safety and efficacy must be conducted before the technique can be tried... | {
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*Siemens Review R& D Special*.
- Kryter, Karl D. 1970. *The Effects of Noise on Man*. New York: Academic Press.
- Lipscomb, David M. 1974. *Noise: The Unwanted Sound*. Chicago, IL: Nelson-Hall.
- Manci, Karen M., Gladwin, Douglas N., Villella, Rita, and Cavendish, Mary G. 1988. *Effects of aircraft noise and sonic boom... | {
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#### 11.1 Introduction
Although people have gathered in large auditoriums and places of worship since the advent of civilization, architectural acoustics did not exist on a scientific basis until a young professor of physics at Harvard University accepted an assignment from Harvard's Board of Overseers in 1895 to cor... | {
"Header 1": "Acoustics of Enclosed Spaces: Architectural Acoustics",
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#### 11.4 Sound Intensity Growth in a Live Room
We now apply the classic ray theory to deal with a sound source operating continuously in an enclosure, which will yield results in fairly good agreement with
Figure 11.5. Geometric configuration for setting up the relationship betwee... | {
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| 0.28 | 0.22 | 0.17 | 0.09 | 0.10 | 0.11 |
| Plaster, gypsum or lime, rough<br>finish on lath | 0.02 | 0.03 | 0.04 | 0.05 | 0.04 | 0.03 |
| Plaster, gypsum or lime, smooth<br>finish on la... | {
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The intensity level in a live room decreases with elapsed time at a constant decay rate D (in dB/s),
$$D = \frac{1.087Ac}{V}.$$
Following Sabine's definition, we define the reverberation time T as the time required for the sound level in the room to decay by 60 dB:
$$T = \frac{60}{D} = \frac{55.2V}{Ac} \tag{11.13... | {
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We have previously not considered the effect of absorption of sound and humidity in air on reverberation times. The volume of air contained in very large auditoriums or a place of worship can absorb an amount of acoustic energy that cannot be neglected as in the case with smaller rooms. If a room is small, the number o... | {
"Header 1": "11.9 Reverberation as Affected by Sound Absorption and Humidity in Air",
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The product IS gives the rate of acoustic energy striking a surface area S; and IS $\cos\theta$ gives that rate for the incidence angle $\theta$ . In an ideal reverberant field, with equal probability for all angles of incidence, the average rate of acoustic energy striking one side of the surface is given by IS/4. ... | {
"Header 1": "11.12 Sound Absorption in Reverberant Field: The Room Constant",
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#### 11.15 Concert Halls and Opera Houses
Three basic shapes exist in the design of large music auditoriums, namely (1) rectangular, (2) fan-shaped, and (3) horseshoe, all of which are illustrated in floor plans of Figure 11.8. A fourth category is the "modified arena", nearly elliptical in shape. The Royal Albert ... | {
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Reverberation Times of Leading Concert Halls and Auditoriums.
| | | | | Reverberation Timea |
|-----------------------------------------------------------------------------------|---------... | {
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(Courtesy of the Seattle Symphony, photograph by Craig Raymond.)
Nesholm) Architects and the acoustical consultant, Cyril M. Harris, combined the shoebox design with state-of-the-art materials to achieve maximum warmth and balance.
The location of Benaroya Hall in a busy sector of Seattle posed special challenges t... | {
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The trellis area that incorporates the network of speakers is 100 m (325 ft) wide by 180 m (600 ft) long. These loudspeakers are strategically suspended at predetermined heights and orientations, in concentric circles outward from the stage. A distributed sound reinforcement system provides direct or "frontal" sound to... | {
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New York: John Wiley & Sons. Beranek, Leo L. July 1992. Concert Hall Acoustics—1992. *Journal of the Acoustical Society of America* 92, 1: 1–39.
- Beranek, Leo. 2004. *Concert and Opera Houses: Music, Acoustics, and Architecture*, 2nd ed. New York: Springer-Verlag. (A tremendous compendium of the acoustical character... | {
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#### 12.1 Introduction
Acoustics constitutes an important factor in building design and in layouts of residences, plants, offices, and institutional facilities. A building not only protects against inclement weather; it must also provide adequate insulation against outside noises from transportation and other sources... | {
"Header 1": "12 Walls, Enclosures, and Barriers",
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#### 12.4 Field Incidence Mass Law
In the situation of transmission loss between two adjoining rooms, the sound source in one room may produce a reverberant field. The incident sound emanating from the source may strike the wall at all angles between 0 and 90°. For field incidence it is customary to assume that the... | {
"Header 1": "12 Walls, Enclosures, and Barriers",
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Panel bending stiffness constitutes the governing factor in low-frequency sound transmission. The panel resonances play the principal role in determining the nature of transmission of higher frequency sounds. The panel may be considered mass-controlled in the frequency range from twice the lowest resonant frequency to ... | {
"Header 1": "12.5 Effect of Frequencies on Sound Transmission through Panels",
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an ideal gas) varies in the following manner:
$$pv^{\gamma} = \text{constant}$$
(12.19)
where v represents the specific volume (equal to the reciprocal of density) and γ , the ratio of specific heats. Differentiating Equation (12.19) gives
$$\frac{dp}{dv} = -\gamma \frac{p}{v}. ag{12.20}$$
Sound waves cause t... | {
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\quad (12.25)$$
#### Example Problem 4
A 6.0 m $\times$ 2.5 m wall is for the most part constructed of 8-cm thick dense poured concrete with a transmission loss of 52 dB at 500 Hz. An opening in the wall is provided for a 2.2 m $\times$ 1.0 m wood door with a transmission loss of 25 dB at 500 Hz. There is a cra... | {
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"token_count": 2042,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
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Manufacturers' catalogues frequently report the one-third octave TL measurements used to evaluate STC. An example of an SIR determination is given in Figure 12.13 for the TL plot of Figure 12.12. Much of the tedium of SIR contour fitting can be eased through the use of computer plotting.
The field incidence mass law,... | {
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"token_count": 2028,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
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(12.30)$$
Combining the last two equations gives the total energy $\delta_2$ density near the wall:
$$\delta_2 = \left(\frac{1}{S_w} + \frac{4}{R_2}\right) \frac{W_2}{c}.\tag{12.31}$$
Equation (12.28) can now be used to eliminate $W_2$ in Equation (12.31) to yield
$$\delta_2 = \frac{4}{R_1} \frac{W_1}{c} \l... | {
"Header 1": "12.5 Effect of Frequencies on Sound Transmission through Panels",
"token_count": 2038,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
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In some cases, a partial enclosure may suffice to shield a worker from excessive exposure to noise. The walls of an enclosure should be constructed of materials that will provide isolation, absorption, and damping—all necessary for effective noise reduction. Moreover, any presence of cracks or leaks can radically reduc... | {
"Header 1": "12.5 Effect of Frequencies on Sound Transmission through Panels",
"token_count": 2022,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
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According to Crèmer (1961), the latter two effects may be taken into account in terms of sound frequency f by the expression
$$\alpha_f = 1.8 \times 10^{-4} \sqrt{f}.$$
The average excess air absorption coefficient $\bar{\alpha}_{ex}$ due to air absorption in a room or enclosure is
$$\alpha_{\rm ex} = k \frac{4... | {
"Header 1": "12.5 Effect of Frequencies on Sound Transmission through Panels",
"token_count": 2022,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
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(12.58)$$
In the case of Figure 12.16, the following path differences exist:
$$d_1 = (r_1 + r_2) - (r_3 + r_4)$$
$$d_2 = (r_5 + r_6) - (r_3 + r_4)$$
$$d_3 = (r_7 + r_8) - (r_3 + r_4)$$
(12.59)
$$D = \sum_{i=1}^{n} \frac{1}{3 + 20N_i}$$
<sup>&</sup>lt;sup>2</sup> In some literature the alternative definition... | {
"Header 1": "12.5 Effect of Frequencies on Sound Transmission through Panels",
"token_count": 2023,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
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For a point source located behind an infinitely long solid wall or berm, the attenuation A' provided by a barrier are given by the following equations, where the arguments of tan and tanh are given in radians:
$$A' = 0 \qquad \text{for } N < -0.1916 - 0.0635b'$$
$$A' = 5(1 + 0.6b') + 20\log\left(\frac{\sqrt{-2\pi N... | {
"Header 1": "12.5 Effect of Frequencies on Sound Transmission through Panels",
"token_count": 2019,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
#### 13.1 Introduction
Loss of hearing constitutes only one of the effects of sustained exposure to excessive noise levels. Noise can interfere with speech and sleep, and cause annoyance and other nonauditory effects. *Annoyance* is quite subjective in nature, rendering it difficult to quantify. Loud steady noise can... | {
"Header 1": "12.5 Effect of Frequencies on Sound Transmission through Panels",
"Header 3": "13 Criteria and Regulations for Noise Control",
"token_count": 1989,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
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It can also be arranged to move the worker to a region, where the noise level averages 86 dB(*A*) or less (i.e., below the OSHA noise level range), for 1.16 h in order to round out 8 h daily on the job.
Annual audiology tests of all workers exposed to this environment are mandated if the noise level equals or exceeds... | {
"Header 1": "12.5 Effect of Frequencies on Sound Transmission through Panels",
"Header 3": "13 Criteria and Regulations for Noise Control",
"token_count": 2024,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
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It was also established that intense low-frequency noise 75 dB or more in region A of Figure 13.5 is apt to cause mechanical vibrations and rattles in lightweight structures. Noise in region B has a low probability to generate such vibration. The RC value of a measured spectrum is defined as the arithmetic average of t... | {
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"Header 3": "13 Criteria and Regulations for Noise Control",
"token_count": 1851,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
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$L_{\rm den}$ and $L_{\rm night}$ are defined as follows:
$$L_{\text{den}} = 10 \log \frac{1}{24} \left( 12 \times 10^{\frac{L_{\text{day}}}{10}} + 4 \times 10^{\frac{L_{\text{evening}} + 5}{10}} + 8 \times 10^{\frac{L_{\text{night}} + 10}{10}} \right)$$
where
$L_{\text{day}} = A$ -weighted average sound leve... | {
"Header 1": "12.5 Effect of Frequencies on Sound Transmission through Panels",
"Header 3": "13 Criteria and Regulations for Noise Control",
"token_count": 2047,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
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NEF is still being used in Canada and in a modified form in Australia.
#### *Noise and Number Index*
The noise and number index (NNI) is a rather subjective method for rating aircraft noise annoyance, developed and used in the United Kingdom. A survey conducted in 1961 of noise in the residential areas within a 10-... | {
"Header 1": "12.5 Effect of Frequencies on Sound Transmission through Panels",
"Header 3": "13 Criteria and Regulations for Noise Control",
"token_count": 2041,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
The second type of impact occurs when the predicted future levels "approach or exceed" the noise abatement criteria of Table 13.3. The criteria of Table 13.3 are listed according to the land-use activity and are in terms of 1-h average sound levels (*L*1*<sup>h</sup>*) or 1-h 10-percentile-exceeded levels.
- 5. Evaluat... | {
"Header 1": "12.5 Effect of Frequencies on Sound Transmission through Panels",
"Header 3": "13 Criteria and Regulations for Noise Control",
"token_count": 2042,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
#### Vehicles are grouped by FHWA into three classes:
- 1. Automobiles (A): All vehicles with two axles and four wheels, including automobiles designed for transportation of nine passengers or fewer, and light trucks and SUVs. Generally, the gross vehicle weight (GVW) is less than 4500 kg (10,000 lb).
- 2. Medium T... | {
"Header 1": "12.5 Effect of Frequencies on Sound Transmission through Panels",
"Header 3": "13 Criteria and Regulations for Noise Control",
"token_count": 1977,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
With reference to Figure 13.7, the *finite roadway segment adjustment* (which depends on the ground cover) is defined as
$$\Delta_{\text{segment}} = 10 \log \int_{\phi_1}^{\phi_2} \frac{1}{\pi} (\cos \phi)^a d\phi$$
(13.16)
where φ<sup>1</sup> and φ<sup>2</sup> are angles in radians at the receiver, as shown in Fig... | {
"Header 1": "12.5 Effect of Frequencies on Sound Transmission through Panels",
"Header 3": "13 Criteria and Regulations for Noise Control",
"token_count": 410,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
4. Over 7%: \Delta_{\text{grade}} = +5 \, \text{dB}(A).
```
If there are one or more rows of buildings present between an observation point and a road, an adjustment for the shielding, $\Delta_{\text{shielding}}$ , by these buildings must be estimated. A rule of thumb can be used in the following manner: if 40–65% o... | {
"Header 1": "12.5 Effect of Frequencies on Sound Transmission through Panels",
"Header 3": "13 Criteria and Regulations for Noise Control",
"token_count": 2019,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
FICON considers noise exposure levels lower than *L*dn = 65 dB to "be compatible with most residential land uses." However, FICON does confess its realization that this limitation may be somewhat too high in highly rural areas where it would be more appropriate to characterize the effects of noise pollution not in acou... | {
"Header 1": "12.5 Effect of Frequencies on Sound Transmission through Panels",
"Header 3": "13 Criteria and Regulations for Noise Control",
"token_count": 2030,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
The police in Lorain, Ohio have been regularly enforcing the law approved in 2002 that prohibits car steros from being audible at 15 m or more from the car. A first offense brings a \$300 fine. A second offense
costs \$400 and the offender's audio equipment gets confiscated as contraband. That equipment is then destr... | {
"Header 1": "12.5 Effect of Frequencies on Sound Transmission through Panels",
"Header 3": "13 Criteria and Regulations for Noise Control",
"token_count": 1988,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
These acts generally cover (a) the erection, construction, alteration, repair, or maintenance of buildings, structures, or roads; (b) the breaking up, opening, or boring under any road or adjacent land in connection with the construction, inspection, maintenance, or removal of public or private works; (c) piling, demol... | {
"Header 1": "12.5 Effect of Frequencies on Sound Transmission through Panels",
"Header 3": "13 Criteria and Regulations for Noise Control",
"token_count": 2028,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
*Journal of the Acoustical Society of America* 89, 1: 221–233.
- Gottlob, D. 1995. Regulations for community noise. *Noise/News International* 3(4): 223– 236.
- Society of Automotive Engineers (SAE). 1991. *Handbook of the Society of Automotive Engineers*. Warrendale, PA: SAE.
- Harris, Cyril M. (ed.). 1991. *Handboo... | {
"Header 1": "12.5 Effect of Frequencies on Sound Transmission through Panels",
"Header 3": "13 Criteria and Regulations for Noise Control",
"token_count": 1985,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
#### 14.1 Introduction
Workplace noise at high levels is detrimental to the welfare of workers. Not only high sound levels can affect hearing and hinder oral communication, but also they detract the employee from performing at peak capacity. In spite of possible economic drawbacks such as the cost of increased mainte... | {
"Header 1": "14 Machinery Noise Control",
"token_count": 2042,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
Three types of centrifugal fans. (Harris, 1991, p. 41.3.).
fan and an axial-flow fan, respectively, along with listing of commonly used nomenclature.
Centrifugal fans come in with a variety of blades. Three types are shown in Figure 14.3. Axial-flow fans divide into three main categories (vaneaxial, tubeaxial, and ... | {
"Header 1": "14 Machinery Noise Control",
"token_count": 2039,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
Centrifugal fan with sound attenuators at inlet and outlet. (Harris, 1991. P. 41.13).
*<sup>a</sup>* BFI <sup>=</sup> blade frequency increment.
1 kPa (4.0 in. water gauge). Table 14.2 lists the relative sound power for a variety of fan types. In reducing all fan noise data to this common base, the concept of speci... | {
"Header 1": "14 Machinery Noise Control",
"token_count": 2041,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
An unfortunate situation is created when the noise from the pump easily transmits through the fluid or piping to other system components.
Pumps generate two types of noise: discrete tones and broadband noise. The pump's fundamental frequency *f <sup>p</sup>* is found from
$$f_p = \frac{n \times N_c}{60} \tag{14.9}$... | {
"Header 1": "14 Machinery Noise Control",
"token_count": 2044,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
A petcock is provided along with a shut-off valve, so that the chamber may be drained of water and vented, thereby reactivating the unit.
There are commercial devices, called *water-hammer arresters*, which are not subject to the limitation of capped pipes, because a metal diaphragm separates the water from the air. ... | {
"Header 1": "14 Machinery Noise Control",
"token_count": 2036,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
If one gear is an internal gear (i.e., a ring gear) the speed ratio is positive, meaning that both gears will rotate in the same angular direction. For a gear train comprised of several gears, the output to input speed ratio is given by
$$\frac{n_{\text{output}}}{n_{\text{input}}} = \prod_{i} \left( \frac{N_{\text{dr... | {
"Header 1": "14 Machinery Noise Control",
"token_count": 2032,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
Gear enclosures or housing can and should be designed to control noise. The enclosure should be isolated so as not to transmit vibration to adjacent structures; and provisions for adequate lubrication of the gears should be included. Resonances of the enclosure should not correspond to the tooth meshing or any other ... | {
"Header 1": "14 Machinery Noise Control",
"token_count": 2022,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
Outer race defect:
$$f_O = \frac{n_O^R v_B}{60} = \frac{(n_O - n_C)v_B}{60}$$
3. Inner race defect:
$$f_I = \frac{n_I^R \nu_B}{60} = \frac{n_C \nu_B}{60}$$
4. Defect or damage to one ball or roller:
$$f_B = \frac{2n_B^R}{60} = \frac{n_B - n_C}{30}$$
5. Imbalance or damage in the separator or cage:
$$f_C =... | {
"Header 1": "14 Machinery Noise Control",
"token_count": 2022,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
In general, for a given rotational speed n, the frequency associated with noise and vibration is given by
$$f = \frac{n}{30}$$
Hz
#### 14.12 Gas-Jet Noise
A most common and also worrisome noise source is the gas jet. This is also referred to as aerodynamic noise, and examples include blowdown nozzles, gas or oil ... | {
"Header 1": "14 Machinery Noise Control",
"token_count": 2045,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
A jet pulse through a nozzle or discharge from HVAC ducts can be modeled as a monopole. In fans and compressors, the turbulent flow generally encounters rotor or stator blades, grids, and baffles; this type of flow can be modeled as a dipole. Quadrupole modeling applies to noise occurring from turbulent mixing in jets ... | {
"Header 1": "14 Machinery Noise Control",
"token_count": 1982,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
Similarly for the other angles, we have
$$DB_{90^{\circ}} = -5 \text{ dB},$$
$L_p(90)^{\circ} = 73.1 - 5 = 68.1 \text{ dB}$
$DI_{180^{\circ}} = -10 \text{ dB},$ $L_p(180^{\circ}) = 73.1 - 10 = 63.1 \text{ dB}$
It becomes apparent from the above example that the jet has a strong directional character that must be ... | {
"Header 1": "14 Machinery Noise Control",
"token_count": 2039,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
But if valves are encased in thick housings, the noise levels are typically 6 to 10 dB lower. The spectral character of the noise resembles that for high-velocity gas jets, i.e., there are peak levels present in the range of 2–8 kHz. In short, it can be expected wherever high-pressure steam and gas flows are regulated ... | {
"Header 1": "14 Machinery Noise Control",
"token_count": 1951,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
Pressure must be continuous at this junction, hence
$$(p_{I1} + p_{R1})_{x=0} = (p_{I2} + p_{R2})_{x=0}$$
(14.54)
Inserting Equations (14.52) and (14.53) into (14.54) gives
$$A_{I1} + A_{R1} = A_{I2} + A_{R2} (14.55)$$
Subscript 1 refers to the left of the junction and subscript 2 refers to the right. Continuit... | {
"Header 1": "14 Machinery Noise Control",
"token_count": 2020,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
The expansion chamber cross-sectional area is
$$B = A \times \frac{B}{A} = 2827 \times 19.95 = 56,399 \,\mathrm{mm}^2$$
If the expansion chamber has a cylindrical cross-section, its inside diameter d is found from
$$B = \frac{\pi d^2}{4}$$
Hence
$$d = \sqrt{\frac{4B}{\pi}} = \sqrt{\frac{4 \times 56,399}{\pi}}... | {
"Header 1": "14 Machinery Noise Control",
"token_count": 2054,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
The inner and outer race diameters are 30 mm and 46 mm, respectively, measured at the point of ball contact. The inner race rotates at 5200 rpm. There are 12 balls in the bearing. Determine
- the noise and vibration frequencies that can occur as the result of imbalance and defects.
- 8. A ball-bearing is constructed ... | {
"Header 1": "14 Machinery Noise Control",
"token_count": 1362,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
#### 15.1 Sound Propagation in Water
Sound waves are absorbed and scattered in water to a much lesser degree than electromagnetic waves. Because of this property sound waves have proven to be particularly useful in detecting distant objects undersea by means of *sonar* (acronym for SOund NAvigation and Ranging). *Pas... | {
"Header 1": "15 Underwater Acoustics",
"token_count": 1828,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
Sound velocity in a natural body of water was first measured in 1827 when the Swiss scientist Jean-Daniel Colladen (1802–1893) and the French mathematician Charles Sturm (1803–1855)
| Expression | Limits | Reference |
|----------------------------... | {
"Header 1": "15 Underwater Acoustics",
"token_count": 2042,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
The effect of latitude on sound-speed profile in the deep sea is shown in Figure 15.3 by profiles for two different locations in the North Atlantic at the same season of the year. At low latitudes (nearer the equator), the velocity minimum occurs at a depth of approximately 3000 ft. At high latitudes the velocity minim... | {
"Header 1": "15 Underwater Acoustics",
"token_count": 2038,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
The absorption of sound in seawater depends on three effects: one is the presence of *shear viscosity*, a classical effect studied by Lord Rayleigh, who derived the following expression for the absorption coefficient:
$$\alpha = \frac{16\pi^2 \mu_s}{3\rho c^3} f^2 \tag{15.3}$$
where
<sup>α</sup> <sup>=</sup> in... | {
"Header 1": "15 Underwater Acoustics",
"token_count": 1992,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
It follows that $\Delta z = R(\cos \theta_1 - \cos \theta_2)$ , and the gradient G is
$$G = \frac{c_2 - c_1}{\Delta z}.\tag{15.8}$$
We can combine the last two Equations with Snell's law of Equation (15.7) which now yields
$$R = -\frac{c_0}{G} = -\frac{c}{G\cos\theta}. (15.9)$$
When G is constant, and hence R ... | {
"Header 1": "15 Underwater Acoustics",
"token_count": 2020,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
#### *Transducer Response*
The effectiveness of a hydrophone in converting sound into an electric signal is called the *response* of the hydrophone. It relates the generated voltage to the acoustic pressure of the sound field. The receiving response of a hydrophone is defined as the voltage produced across the term... | {
"Header 1": "15 Underwater Acoustics",
"token_count": 2015,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
But when the target is just being detected, the signal-to-noise ratio equals the detection threshold DT, i.e.,
$$SL - 2 TL + TS - (NL - DI) = DT$$
(15.15)
Equation (15.15) characterizes the active-sonar equation as an equality in terms of the *detection threshold*. In recognizing that only a portion of the noise po... | {
"Header 1": "15 Underwater Acoustics",
"token_count": 2041,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
For example, the target will be first detected at a range of 10 miles according to the line component at frequency *f*1. But suppose it is required that three spectral lines must appear on the display before a detection is called; the range would be reduced to 4 miles and the lines at frequencies *f*1, *f*2, and *f*<su... | {
"Header 1": "15 Underwater Acoustics",
"token_count": 2029,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
Thus, precise calculations to, say the nearest tenth of a decibel are exercises in futility, and the solutions must be considered "best guesses" or "most probable" values.
#### 15.17 Theoretical Target Strength of a Sphere
Consider a sphere of radius*r* as the subject target. As we shall see, the effect of the puls... | {
"Header 1": "15 Underwater Acoustics",
"token_count": 2051,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
An Interim Report on the Sound Velocity Distribution in the North Atlantic Ocean. *U.S. Navy Oceangoing Office Technical Report 171*.
- Urick, Robert J. 1962. Generalized form of the sonar equations. *Journal of the Acoustical Society of America* 34: 547.
- Urick, Robert J. 1983. *Principles of Underwater Sound*, 3rd e... | {
"Header 1": "15 Underwater Acoustics",
"token_count": 921,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
#### 16.1 Introduction
As a subcategory of acoustics, *ultrasonics* deals with acoustics beyond the audio frequency limit of 20 kHz. Although ultrasonics has been employed for most of the twentieth century, the tempo of new and improved applications has reached virtually explosive proportions only in the past few yea... | {
"Header 1": "16 Ultrasonics",
"token_count": 2021,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
The 350-collision average indicates that only one of the 350 collisions possesses the proper geometry and energy to execute a transfer of one quantum of rotational energy. The number of collisions necessary, on the average, to engender the transfer one quantum of rotational energy is termed the *collision number Z*. Wh... | {
"Header 1": "16 Ultrasonics",
"token_count": 1922,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
After the transient dies out, then we have
$$T_{tr} - T_0 = (1 + i\omega t)(T' - T_0)$$
or
$$T' - T_0 = \frac{T_{tr} - T_0}{1 + i\omega\tau}$$
which can also be rewritten as
$$\frac{dT'}{dT_{tr}} = \frac{1}{1 + i\omega t}$$
The effective specific heat can be established from
$$dE = (C_v)_{eff} dT_{tr} = \... | {
"Header 1": "16 Ultrasonics",
"token_count": 2010,
"source_pdf": "datasets/websources/Physics_v1/Physics/pdf_esp_198.pdf"
} |
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