What is the sound intensity of a whisper at a distance of 3.5 m, in W/m2?  What is the corresponding sound intensity level in dB? 

Expert Answers
valentin68 eNotes educator| Certified Educator

The decibel level intensities of different sounds are tabulated. Since decibel is a logarithmic quantity the intensities of sounds tabulated starts from about the hearing threshold (which is also the reference level of sound intensity `I_0 =10^-12 W/m^2` or 0 dB), to a jet engine aircraft a few tens of meter away (140 dB) and to the strongest possible sound (far beyond pain and hearing loss) (195 dB). This highest level of sound is attained when all the air molecules oscillates one way, or otherwise said when for a moment all the air at pressure of 1 atmosphere is for a moment depleted.

For a whisper the sound level is about 35 dB, between a quiet bedroom and a quiet library.

`L =35 dB`

Since the definition of sound level is logarithmic (the intensity reference is above)

`L =10*log(I/I_0)`

`35 =10*log(I/10^-12)`


`I =10^(3.5-12) =10^-8.5 =3.16*10^-9 W/m^2`

Of course this is only an approximate evaluation since for the exact value you need to specify the initial power of the sound at the point it has been emitted.