Question

At a distance of 13.0 m from a point source, the intensity level is measured to be 65 dB. At what distance from the source will the intensity level be 32.5 dB?

Answer 1

Sound intensity (L) and distance ( r ) are related by -

L​​​​​1 - L​​​​2 =.  ​​​​​​20log( r​​​1/ r​​​2 )

Here r_{​​​​​​1} = 13.0 m , L_{​​​​​1} = 65 db , L_{​​​​​​2} = 32.5 db

Readjusting the above equation we gets -

( r_​​​1/ r_​​​2 ) = 10^{(L_​​​1​​​- L_​2​)/20}

=. 10^1.625. =. 42.17

( after putting values and calculation )

13 / r_{​​​​​​2} = 42.17

r_{​​​​​​2} = 13 / 42.17

=. 0.30827 m .

The intensity level will be 32.5 db at a distance of 0.30827 m.

Please rate good if you are satisfied with the solution

Thank you .