Answer
(a) Right in front of the trumpet, the intensity level is $138~dB$
(b) At a distance of 10.0 m, the intensity level is $88~dB$
Work Step by Step
(a) We can find the intensity:
$I = \frac{P}{A}$
$I = \frac{P}{\pi~r^2}$
$I = \frac{0.800~W}{(\pi)~(0.0635~m)^2}$
$I = 63.15~W/m^2$
We can find the sound intensity level:
$\beta = 10~log\frac{I}{I_0}$
$\beta = 10~log\frac{63.15~W/m^2}{1.0\times 10^{-12}~W/m^2}$
$\beta = 138~dB$
Right in front of the trumpet, the intensity level is $138~dB$
(b) We can find the intensity at a distance of 10.0 m:
$I = \frac{P}{A}$
$I = \frac{P}{4\pi~r^2}$
$I = \frac{0.800~W}{(4\pi)~(10.0~m)^2}$
$I = 6.366\times 10^{-4}~W/m^2$
We can find the sound intensity level:
$\beta = 10~log\frac{I}{I_0}$
$\beta = 10~log\frac{6.366\times 10^{-4}~W/m^2}{1.0\times 10^{-12}~W/m^2}$
$\beta = 88~dB$
At a distance of 10.0 m, the intensity level is $88~dB$
