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Sound
Sound Intensity and Level
Physics Textbooks Boundless Physics Sound Sound Intensity and Level
Physics Textbooks Boundless Physics Sound
Physics Textbooks Boundless Physics
Physics Textbooks
Physics
Concept Version 7
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Intensity

Sound Intensity is the power per unit area carried by a wave. Power is the rate that energy is transferred by a wave.

Learning Objective

  • Calculate sound intensity from power


Key Points

    • Sound intensity can be found from the following equation: $I=\frac{{{\Delta}p}^2}{2\rho{v_w}}$Δ p - change in pressure, or amplitude ρ - density of the material the sound is traveling through vw - speed of observed sound.
    • The larger your sound wave oscillation, the more intense your sound will be.
    • Although the units for sound intensity are technically watts per meter squared, it is much more common for it to be referred to as decibels, dB.

Terms

  • decibel

    A common measure of sound intensity that is one tenth of a bel on the logarithmic intensity scale. It is defined as dB = 10 * log10(P 1/P 2), where P1 and P2 are the relative powers of the sound.

  • amplitude

    The maximum absolute value of some quantity that varies.


Example

    • Use the following information to calculate (1) the sound intensity and (2) the decibel level. p = 0.656 Pavw= 331 m/s2, at 0 degrees Celsius. (Air pressure at 0C is 1.29 kg/m3)1. $I=\frac{{\Delta}p{^2}}{2\rho{v_w}}\\ I=\frac{{{0.656 Pa}^2}}{2*1.29{\frac {kg}{m^3}}*331{\frac ms}}\\ I=5.04*10^{-4} \frac W{m^2}$2. Now we want to convert this intensity into decibel level:$\beta = 10 log_{10}\frac {5.04*10^{-4}}{1*10^(-12)}\\ \beta = 10 log_{10}5.04*10^8\\ \beta = 10*8.70dB\\ \beta = 87dB$

Full Text

Overview of Intensity

Sound Intensity is the power per unit area carried by a wave . Power is the rate that energy is transferred by a wave.

Sound Intensity and Decibels

The equation used to calculate this intensity, I, is:$I=\frac PA$Where P is the power going through the area, A. The SI unit for intensity is watts per meter squared or,$\frac W{m^2}$. This is the general intensity formula, but lets look at it from a sound perspective.

Sound Intensity

Sound intensity can be found from the following equation:$I=\frac{{{\Delta}p}^2}{2\rho{v_w}}$Δp - change in pressure, or amplitudeρ - density of the material the sound is traveling throughvw - speed of observed sound.Now we have a way to calculate the sound intensity, so lets talk about observed intensity. The pressure variation, amplitude, is proportional to the intensity, So it is safe to say that the larger your sound wave oscillation, the more intense your sound will be. This figure shows this concept.

Sound Intensity

Graphs of the gauge pressures in two sound waves of different intensities. The more intense sound is produced by a source that has larger-amplitude oscillations and has greater pressure maxima and minima. Because pressures are higher in the greater-intensity sound, it can exert larger forces on the objects it encounters

Although the units for sound intensity are technically watts per meter squared, it is much more common for it to be referred to as decibels, dB. A decibel is a ratio of the observed amplitude, or intensity level to a reference, which is 0 dB. The equation for this is:$\beta = 10 log_{10}\frac I{I_0}$β - decibel levelI - Observed intensityI0- Reference intensity.For more on decibels, please refer to the Decibel Atom.

For a reference point on intensity levels, below are a list of a few different intensities:

  • 0 dB, I = 1x10-12 --> Threshold of human hearing
  • 10 dB, I = 1x10-11 --> Rustle of leaves
  • 60 dB, I = 1x10-6 --> Normal conversation
  • 100 dB, I = 1x10-2 --> Loud siren
  • 160 dB, I = 1x104--> You just burst your eardrums
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