Question

In October 1991, the Sacramento City Council adopted a law to reduce the allowed sound intensity level of the much despised leaf blowers from their current level of about 95 dB to 70 dB by May 1992.
With the new law, what is the ratio of the new allowed intensity to the previously allowed intensity?

Answer 1

Prevous allowed intensity level L = 95 dB

     L = 10 log ( I / Io)

    95 = 10 log ( I / Io)

   9.5 = log( I / Io)

I /Io = 10^9.5

I = Io * 10^9.5

   = 10^-12 * 10^9.5

   = 10^-2.5   W / m^ 2

New allowed intensity level L ' = 70 dB

     L ' = 10 log ( I '/ Io)

    70 = 10 log ( I ' / Io)

   7 = log( I ' / Io)

I ' /Io = 10^7

I ' = Io * 10^7

   = 10^-12 * 10^7

   = 10^-5   W / m^ 2

the ratio of the new allowed intensity to the previously allowed intensity = I ' / I

                           = 10^-5 / 10^-2.5

                           = 10^-2.5

                           = 3.162*10^-3