A point source emits sound waves isotropically. The intensity of the waves 2.50 m from the source is $$1.91 \times 10^{-4} W/m^{2}$$. Assuming that the energy of the waves is conserved , find the power of the source.
The intensity is the rate of energy flow per unit area perpendicular to the flow.
The rate at which energy flow across every sphere centered at the source is
the same, regardless of the sphere radius, and is the same as the power output of the source.
If $$P$$ is the power output and $$I$$ is the intensity a distance $$r$$ from the source,
then $$P = IA = 4\pi r^{2} I$$, where $$A\left (= 4 \pi r^{2} \right )$$ is the surface area of a sphere of radius $$r$$. Thus
$$P = 4\pi\left ( 2.50 \space m \right )^{2} \left (1.91 \times 10^{-4} \space W/m^{2} \right ) = 1.50 \times 10^{-2} \space W$$
Two atmospheric sound sources A and B emit isotropically at constant power. The sound levels $$\beta$$ of their emissions are plotted in Fig. 17-40 versus the radial distance $$r$$ from the sources. The vertical axis scale is set by $$\beta_1 = 85.0 \space dB$$ and $$\beta_2 = 65.0 \space dB$$. What are (a) the ratio of the larger power to the smaller and (b) the sound level difference at $$r = 10 \space m$$?
The sound intensity is $$ 0.0080 \mathrm{W} / \mathrm{m}^{2} $$ at a distance of $$ 10 \mathrm{m} $$ from an isotropic point source of sound. What is the power of the source?
A loudspeaker at a rock concert generates $$10^{-2}\ W/m^2$$ at $$20\ m$$ at a frequency of $$1\ kHz$$. Assume that the speaker spreads its energy uniformly in all directions.What is the total acoustic power output of the speaker?