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Oscillations

# Two sinusoidal machines are positioned the same distance from a worker . The intensity of sound delivered by each machine at the location of the worker is $\;2.0 \times 10^{-7}\;w/m^2\;$ . Find the sound level heard by the worker (i) when one machine is operating (ii) when both machines are operating

$(a)\;53\;fB\;,37\;fB\qquad(b)\;53\;fB\;,56\;fB\qquad(c)\;53\;fB\;,60\;fB\qquad(d)\;None$

Answer : (b) $\;53\;fB\;,56\;fB$
Explanation :
$I_{0}=10^{-12}\;w/m^{2}$
$\beta_{1}=10 log (\large\frac{2.0\times10^{-7}\;w/m^2}{10^{-12}\;w/m^2})$
$=10 log (2 \times 10^{5})$
$=53\;fB$
When both machine are operating the intensity is doubled $\;4\times 10^{-7}\;w/m^2$
$\beta_{2}=10 log(\large\frac{4 \times 10^{-7}}{10^{-12}})=10 log (4 \times 10^{5})$
$=56\;fB$