What is the sound level in dB for a sound whose intensity is 5.0 × 10 − 6 w a t t s / m 2 ?

Question

What is the sound level in dB for a sound whose intensity is   5.0  ×  10  −  6  w  a  t  t  s      /        m          2      ?

Brenton Gay · Accepted Answer

The range of sound intensity that humans can detect is so large ( spans 13 orders of magnitude). The intensity of the faintest sound that is audible is called the Threshold of Hearing. This has an intensity of about   1  ×      10          −      12        W      m          −      2      Because it is difficult to gain intuition for numbers in such a huge range it is desirable that we come up with a scale to measure sound intensity that falls within a range of 0 and 100. That is the purpose of the decibell scale (dB).Since logarithm has the property of taking in huge number and returning a small number the dB scale is based on logarithmic scaling. This scale is defined such that the Threshold of Hearing intensity has a sound intensity level of 0.The intensity level in dB of a sound of intensity I is defined as:  (  10  d  B  )      log          10        ⁡  (      I          I              0              )  ;      I          0      -intensity at the threshold of hearing .This problem:  I  =  5  ×      10          −      6        W      m          −      2        ;      I          0        =  1  ×      10          −      12        W  ∗      m          −      2      The sound intensity level in dB is:  (  10  d  B  )      log          10        ⁡  (            5      ×              10                  −          6                    W              m                  −          2                            1      ×              10                  −          12                    W              m                  −          2                      )  =  66.99  d  B

What is the sound level in dB for a sound whose intensity is 5.0 x 10-6 watts/m2?

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