## College Physics (4th Edition)

(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 $88~dB$
(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 $88~dB$