Question

An outside loudspeaker (considered a small source) emits sound waves with a power output of 106 W. (a) Find the intensity 11.2 m from the source W/m

Answer 1

The intensity \( I \) of sound waves at a given distance \( r \) from a small source can be calculated using the formula:

\[ I = \frac{P}{4\pi r^2} \]

Where \( P \) is the power output of the source and \( r \) is the distance from the source. Plugging in the given values:

\( P = 106 \) W
\( r = 11.2 \) m

The intensity \( I \) at a distance of 11.2 m would be:

\[ I = \frac{106}{4\pi \cdot (11.2)^2} \approx 0.221 \, \text{W/m}^2 \]