# A sound wave traveling in 20ºC air has a pressure amplitude of 0.5 Pa. What is the intensity of the wave?

Feb 21, 2015

I=3.03×10^(-4)W/m^2.

Intensity is defined as power over an area. It's given by

$I = \frac{P}{A}$

where
$I \to$ intensity; $\frac{W}{m} ^ 2$
$P \to$ power; $W$
$A \to$ area; ${m}^{2}$

The intensity of a sound wave is given by the following eq'n:

$I = {\left(\Delta p\right)}^{2} / \left(2 \rho {v}_{w}\right)$

where
$I \to$ intensity; $\frac{W}{m} ^ 2$
$\Delta p \to$ pressure variation/pressure amplitude $P a \mathmr{and} \frac{N}{m} ^ 2$
$\rho \to$ density of material; $\frac{k g}{m} ^ 3$
${v}_{w} \to$ speed of sound in medium; $\frac{m}{s}$

Given this equation, along with constants, you can substitute your values and solve.

The constant for the speed of sound in air at 20*C is 343$\frac{m}{s}$.
The density of air is 1.2041 $\frac{k g}{m} ^ 3$.

$I = {0.5}^{2} / \left(2 \left(1.2041\right) \left(343\right)\right) = 3.026588214271792 \cdot {10}^{- 4}$
$3.03 \cdot {10}^{- 4} \frac{W}{m} ^ 2.$

I use my Physics for Scientists and Engineers (9th ed.) and my professor's notes to find equations and constants for most problems, including this one. Good luck!