Progressive wave : Intensity and sound level

Progressive wave : Intensity and sound level

If we hear the sound produced by violin, flute or harmonium, we get a pleasing sensation in the ear, whereas the sound produced by a gun, horn of a motor car etc. produce unpleasant sensation in the ear.

The loudness of a sound depends on intensity of sound wave and sensitivity of the ear.

The intensity is defined as the amount of energy crossing per unit area per unit time perpendicular to the direction of propagation of the wave.

Intensity is measured in W m^?2.

The intensity of sound depends on (i) Amplitude of the source (I α a²), (ii) Surface area of the source (I α A), (iii) Density of the medium (I α ρ), (iv) Frequency of the source (I α n²) and (v) Distance of the observer

from the source (I α 1/r²).

The lowest intensity of sound that can be perceived by the human ear is called threshold of hearing. It is denoted by I_o.

For sound of frequency 1 KHz, I_o =10^?12  W m^?2. The level of sound  intensity is measured in decibel. According to Weber-Fechner law,

decibel level (β) =  log₁₀[I/I₀]

where I_o is taken as 10^?12 W m^?2 which corresponds to the lowest sound intensity that can be heard. Its level is 0 dB. I is the maximum intensity that an ear can tolerate which is 1W m^?2 equal to 120 dB.

β = 10 log₁₀(1/10^-12)

β = 10 log₁₀(10¹²)

β = 120 dB

List gives the decibel value and power density (intensity) for various sources.

Intensity of sound sources

Source of sound   Sound         Intensity

          intensity(dB)        (W m^?2)

Threshold of pain 120   1

Busy traffic 70      10^?5

Conversation        65      3.2 ? 10^?6

Quiet car     50      10^?7

Quiet Radio          40      10^?8

Whisper      20      10^?10

Rustle of leaves    10      10^?11

Threshold of hearing      0        10^?12