Sound intensity Formula

The intensity of sound is defined as the sound power per unit area. The usual context is the measurement of the intensity of sound in the air where the listener is. It also depends on the surface of the sound source. The increase in the amplitude of the source and that of the vibrating surface causes the kinetic energy of the mass of air in contact with it to increase simultaneously; this kinetic energy increases, in effect, with the mass of air that is put into vibration and with its average speed (which is proportional to the square of the amplitude). The intensity of perception of a sound by the ear also depends on its distance from the sound source. Finally, the intensity also depends on the nature of the elastic medium between the source and the ear. Non-elastic media, such as wool, felt, etc., considerably weaken the sounds. The intensity of the sound that is perceived subjectively is what is called sonority and allows sounds to be arranged on a scale from the loudest to the weakest.

sound intensity = acoustic power / normal area to the direction of propagation.

The equation is:

I = P/A.

We have,

I = sound intensity.

P = acoustic power.

A = normal area to the direction of propagation.

The physiological intensity or sound sensation of a sound is measured in decibels (dB). For example, the hearing threshold is 0 dB, the physiological intensity of a whisper corresponds to about 10 dB and the noise of waves on the coast to about 40 dB. The scale of sound sensation is logarithmic, which means that an increase of 10 dB corresponds to an intensity 10 times greater for example, the noise of the waves on the coast is 1,000 times more intense than a whisper, which equals an increase of 30 dB.

Due to the extension of this audibility interval, to express sound intensities is used a scale whose divisions are powers of ten and whose unit of measurement is the decibel (dB).

The conversion between intensity and decibels follows this equation:

The intensity in decibels = 10 * log₁₀ (intensity/ intensity of zero decibels)

The equation is:

S = 10*log(I/I₀)

s = intensity in decibels.

I = sound intensity.

I₀ = sound intensity of zero decibels= 10^-12 W/m^-2

Sound intensity Questions:

1)What is the level of sound sensation in decibels corresponding to an intensity wave 10^-10 W/m^-2?

Answer: The first thing to notice is that they are already giving us the intensity of sound, so we can easily calculate the sound sensation.

I = 10^-10 W/m^-2.

S = 10*log(I/I₀) = 10*log(10^-10W/m^-2/0-12 W/m^-2) = 20 dB

S = 20 dB.

2)From the previous exercise, determine the power generated if the normal propagation area is 20km².

Answer: Using the intensity of sound given in the previous exercise.

I = 10^-10 W/m^-2.

A = 20*10⁶m².

I = P/A--→

P = I*A = 10^-10 W/m^-2* 20*10⁶m² = 2*10^-3W.