# Intensity

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

#### 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

• 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.

• The maximum absolute value of some quantity that varies.

#### Examples

• 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$

#### Figures

1. ##### 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

## Overview of Intensity

Sound Intensity is the power per unit area carried by a wave Figure 2. Power is the rate that energy is transferred by a wave.

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. Figure 1

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

#### Key Term Glossary

amplitude
The maximum absolute value of some quantity that varies.
##### Appears in these related concepts:
atom
The smallest possible amount of matter which still retains its identity as a chemical element, now known to consist of a nucleus surrounded by electrons.
##### Appears in these related concepts:
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.
##### Appears in these related concepts:
eardrum
A thin membrane that separates the outer ear from the middle ear and transmits sound from the air to the malleus.
##### Appears in this related concept:
energy
A quantity that denotes the ability to do work and is measured in a unit dimensioned in mass × distance²/time² (ML²/T²) or the equivalent.
##### Appears in these related concepts:
equation
An assertion that two expressions are equal, expressed by writing the two expressions separated by an equal sign; from which one is to determine a particular quantity.
##### Appears in these related concepts:
normal
A line or vector that is perpendicular to another line, surface, or plane.
##### Appears in these related concepts:
oscillation
the act of oscillating or the state of being oscillated
##### Appears in these related concepts:
power
A measure of the rate of doing work or transferring energy.
##### Appears in these related concepts:
pressure
the amount of force that is applied over a given area divided by the size of that area
##### Appears in these related concepts:
SI units
International System of Units (abbreviated SI from French: Le Système international d'unités). It is the modern form of the metric system.
##### Appears in these related concepts:
watt
In the International System of Units, the derived unit of power; the power of a system in which one joule of energy is transferred per second.
##### Appears in these related concepts:
wave
A moving disturbance in the energy level of a field.