Answer
(a) $69.5dB$
(b) less than
Work Step by Step
(a) We know that
$\beta=(10dB)(\frac{I}{I_{\circ}})$
$\implies \beta=(10dB)log(\frac{20I}{I_{\circ}})$
$\implies \beta=10log(\frac{20}{I_{\circ}})-10logI$
We plug in the known values to obtain:
$82.5dB=10log(\frac{20}{10^{-12}W/m^2})+10logI$
This simplifies to:
$I=8.89\times 10^{-6}W/m^2$
Now the intensity level of violin is is given as
$\beta_1=10log\frac{I}{I_{\circ}}$
We plug in the known values to obtain:
$\beta_1=10log(\frac{8.89\times 10^{-6}W/m^2}{10^{-12}W/m^2})$
$\implies \beta_1=69.5dB$
(b) We know that if the number of the violins is doubled then the intensity level increases by 2 while in dB it increases by $10log 2$. Hence, the resultant intensity level is $69.5dB+10log2=72.5dB$
We conclude that the intensity level is less than $165dB$.
