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 v_w - 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 Pav_w= 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 throughv_w - 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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