(a) What is the intensity of a sound that has a level 7.00 dB lower than a 4.00 × 10 − 9 W / m 2 sound? (b) What is the intensity of a sound that is 3.00 dB higher than a 4.00 × 10 − 9 W / m 2 sound?

Question

(a) What is the intensity of a sound that has a level 7.00 dB lower than a   4.00  ×      10          −      9        W      /        m          2       sound? (b) What is the intensity of a sound that is 3.00 dB higher than a   4.00  ×      10          −      9        W      /        m          2       sound?

Daniella Cochran · Accepted Answer

Sound intensity level in decibels is:  β  =  10  ∗  log  ⁡      I          I              0            Where       I          0        =      10          −      12        W      /        m          2      , the limit of audiable sound and       I          1        =  4  ∗      10          −      9        W      /        m          2      After solving the equation, we get that:      β          1        =  36  d  BFor a sound that has 7 dB lower sound, intensity can be calculated as:  29  =  10  ∗  log  ⁡  (            I              a                    I              0              )Solving this equation gives.      I          a        =  8  ∗      10          −      10        W      /        m          2      For a sound that has 3 dB lower sound, intensity can be calculated as:  39  =  10  ∗  log  ⁡  (            I              b                    I              0              )Solving this equation gives:      I          b        =  8  ∗      10          −      9        W      /        m          2      Result:      I          a        =  8  ∗      10          −      10        W      /        m          2            I          b        =  8  ∗      10          −      9        W      /        m          2

(a) What is the intensity of a sound that has a level 7.00 dB lower than a 4.0010^(−9)W/m^2 sound? (b) What is the intensity of a sound that is 3.00 dB higher than a 4.0010^(−9)W/m^2 sound?

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