What is the variation of pressure in the sound wave if the sound intensity is 3.85 times 10^{-8}...

Question:

What is the variation of pressure in the sound wave if the sound intensity is {eq}3.85 times 10^{-8} W/m^2 {/eq} the speed of sound is 343 m/s and the density of air is {eq}1.2 kg/m^3? {/eq}

The pressure of sound wave:

The variation in the pressure of the sound wave is directly proportional to the intensity of the wave. The intensity of the wave is given by the ratio of the power of the source to the surface area.

Given data:

• Intensity of the sound wave {eq}\rm (I) = 3.85 \times 10^{-8} \ W /m^{2} {/eq}
• Speed of the sound {eq}\rm (V) = 343 \ m/s {/eq}
• Density of the air {eq}\rm (\rho_{a}) =1.2 \ kg/m^{3} {/eq}

Now, the intensity of the wave is given by

{eq}\begin{align} \rm I &= \rm \dfrac{(\delta P)^{2}}{2\rho_{a} V} \\ \rm (3.85 \times 10^{-8} \ W/m^{2}) &= \rm \dfrac{(\delta P)^{2}}{2 \times 1.2 \ kg/m^{3} \times 343\ m/s } \\ \rm \delta P &= \rm \boxed{ 5.63 \times 10^{-3} \ Pa }\\ \end{align} \ {/eq}