Intensity and Amplitude Relationship

4 Key excerpts on "Intensity and Amplitude Relationship"

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  eBook - ePub

  Fundamental Physics of Ultrasound

  • Shutilov, Vladimir Alexandrovich Shutilov, Yelena Vladimirovna Tcharnaya(Authors)
  • 2020(Publication Date)
  • CRC Press

    (Publisher)

  Since the acoustic energy propagates with the velocity of sound c 0, the intensity is determined by multiplying the energy density w ¯ by c 0, which gives l = wc 0 = v max 2 2 ρ 0 c 0 = p max 2 2 1 ρ 0 c 0 = v max p max 2, (III.21) or in terms of effective values: l = v eff 2 ρ 0 c 0 = p eff 2 / (ρ 0 c 0) = v eff p eff. The intensity, in contrast to the energy density, is a vector quantity characterizing the directed flow of energy. Thus, if the energy densities of the forward and backward waves add on superposition, then the intensities are subtracted, so that, for example, the total intensity in the field of two oppositely traveling waves with identical amplitude equals zero. In addition to the intensity, we can introduce the concept of the total flux of acoustic energy or the acoustic radiation power through the surface S defined as D = lS = v max 2 2 ρ 0 c 0 S = p max 2 2 S ρ 0 c 0 = (p max S) v max 2. (III. 22a) This equation assumes that the intensity is constant over the surface S. The acoustic power can in general be determined by integrating over the area: D = ∫ S [ I (S) ⋅ n ] dS. (III. 22b) Thus the radiation intensity represents the specific power, i.e., the power per unit surface area. If the power is measured in watts and the unit surface area is 1 cm 2, then the unit of measurement of intensity is 1 W / cm 2, which is the most commonly employed unit. We note that the equations for the ultrasonic intensity (III.21) or the acoustic power (III.22a) are analogous to the equations for the ac power dissipated as Joule heat in an ohmic resistance R e : D = l max 2 2 R e = U max 2 2 R e = l max U max 2 = I eff U eff. The analog of the current is the particle velocity v, the analog of the electrical voltage U is the acoustic pressure force F = pS, and the analog of the ohmic resistance R e is the acoustic resistance ρ 0 c 0 S

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  eBook - ePub

  Acoustics and Psychoacoustics

  • David M. Howard, Jamie Angus(Authors)
  • 2017(Publication Date)
  • Routledge

    (Publisher)

  Figure 1.10 .

  Figure 1.10  Sound Intensity

  1.2.1 Sound Intensity Level

  The sound intensity represents the flow of energy through a unit area. In other words, it represents the watts per unit area from a sound source, and this means that it can be related to the sound power level by dividing it by the radiating area of the sound source. As discussed earlier, sound intensity has a direction that is perpendicular to the area that the energy is flowing through; see Figure 1.10 . The sound intensity of real sound sources can vary over a range, which is greater than one million-million (1012 ) to one. Because of this, and because of the way we perceive the loudness of a sound, the sound intensity level is usually expressed on a logarithmic scale. This scale is based on the ratio of the actual power density to a reference intensity of 1 picowatt per square meter (10−12 W m−2 ). Thus the sound intensity level (SIL) is defined as:

  S I L = 1 0 l o g 1 0 ( I a c t u a l I r e f )

  (1.18)

  The symbol for power in watts is W.

  • where I
    actual
    = the actual sound power density level (in W m−2 )
  •    and I
    ref
    = the reference sound power density level (10−12 W m−2 )

  The factor of 10 arises because this makes the result a number in which an integer change is approximately equal to the smallest change that can be perceived by the human ear. A factor-of-10 change in the power density ratio is called the bel; in Equation 1.18 this would result in a change of 10 in the outcome. The integer unit that results from Equation 1.18 is therefore called the decibel (dB). It represents a

  10

  10

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  eBook - ePub

  Foundations of Engineering Acoustics

  • Frank J. Fahy(Author)
  • 2000(Publication Date)
  • Academic Press

    (Publisher)

  square of sound pressure. It is of great importance in theoretical and experimental studies, and for measurement methodology, because it is a conserved quantity, unlike the first-order quantities pressure and particle velocity. As a sound wave propagates, the sum of its total kinetic and potential energies must be conserved in the absence of dissipative processes. The rate of generation of sound energy, termed ‘sound power’, is the primary measure of the strength, or output, of a source of sound.

  At this point, it is apposite to impress upon the reader that the human audio system does not respond to intensity, but to sound pressure, and that intensity calculation or measurement is essentially a means to an end in terms of noise control. It must also be understood that, contrary to the impression given by many acoustics textbooks, there is generally no simple relation between sound intensity and sound pressure in practical situations.

  When sound energy is generated by a source in free field it flows radially outwards (except very close to complex sources) and therefore spreads over an increasing area as it travels. The measure of the rate of flow of sound energy per unit of area oriented normal to a wavefront is termed ‘sound intensity’ [5.1 ]. It is more precisely expressed as ‘sound power flux density’.

  Sound intensity will be subsequently shown to equal the product of sound pressure (a scalar) and particle velocity (a vector). Hence it is a vector quantity, possessing both magnitude and direction. In a linear sound field, particle velocity is derivable from sound pressure (alternatively, as shown in textbooks on fluid dynamics, both are derivable from velocity potential). Therefore knowledge of the sound intensity vector does not, in principle, offer any more information than is contained in the pressure field. However, the conservative nature of energy offers approaches to the theoretical modelling, analysis and computation of sound fields as alternatives to the ‘classical’ approach involving direct solution of the wave equation. These alternative approaches are often simpler and more explicit than the latter, as we shall find in Chapter 9

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  eBook - ePub

  Sound FX

  Unlocking the Creative Potential of Recording Studio Effects

  • Alex Case(Author)
  • 2012(Publication Date)
  • Routledge

    (Publisher)

  isobars, the rings of sound radiating outward from the sound source indicate the spatial distribution of points of equivalent pressure. This is a helpful image for audio engineers; it works in comics too.

  The amplitude versus distance expression of sound leads to another fundamental property of waveforms: wavelength, which is the distance traveled during exactly one cycle. Drive 55 miles per hour for one hour, and the distance covered is exactly 55 miles. Distance traveled can be calculated through the multiplication of speed by time. The speed of sound in air (under normal temperature and pressure) is 344 m/s. The always-friendly metric system does fail us a bit here, as the speed of sound in feet per second is about 1,130 ft/s. For rock and roll, it is often acceptable to round this down to an even 1,000 ft/s.

  Figure 1.5 A snapshot in time shows amplitude over a distance from sound source to receiver.

  To calculate the wavelength, then, multiply this speed-of-sound figure by the appropriate amount of time. Recalling that the time it takes a wave to complete exactly one cycle is, by definition, its period:

  where λ=wavelength, c =speed of sound, and T =period.

  Expressing wavelength as a function of frequency (f) requires substitution of frequency for period. Using Equation 1.2 :

  Precise calculations are straightforward, but it is worth noting that wavelengths can be juggled in one′s head in the heat of a recording session without resorting to pencil, paper, or calculator, provided the speed of sound sticks to the fair approximation of 1,000 feet per second.

  A representative middle frequency is a 1-kHz sine wave. Using Equation 1.4

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