Intensity Of Sound Waves - Practice Questions & MCQ

The intensity of Periodic sound waves -

The intensity I of a wave is defined as the power per unit area, as the rate at which the energy transported by the wave transfers through a unit area A perpendicular to the direction of travel of the wave.

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

In this case, the intensity is therefore $I=\frac{1}{2}\rho v(\omega A{)}^2$

Also, for any sound waves -

$\begin{array}{rl}\mathrm{\Delta }{P}_m& =ABk\\ A& =\frac{\mathrm{\Delta }{P}_m}{Bk}\end{array}$

Put this value in the equation of intensity

$I=\frac{1}{2}\rho v{\omega }^2{\left(\frac{\mathrm{\Delta }{P}_m}{Bk}\right)}^2=\frac{1}{2}\rho v{\omega }^2\frac{\mathrm{\Delta }{P}_m^2}{B^2{k}^2}$

As $k=\omega /v$ and $B=v^2\rho$

$\therefore I=\frac{1}{2}\rho v{\omega }^2\frac{\mathrm{\Delta }{P}_m^2}{B^2\frac{{\omega }^2}{v^2}}=\frac{v\mathrm{\Delta }{P}_m^2}{2B}=\frac{\mathrm{\Delta }{P}_m^2}{2\rho v}$
 

Let us consider a source that emits sound equally in all directions, the result is a spherical wave. The figure given below shows these spherical waves as a series of circular arcs concentric with the source. Each circular arc represents a surface over which the phase of the wave is constant. We call such a surface of constant phase a wavefront. The distance between adjacent wavefronts that have the same phase is called the wavelength  of the wave. The radial lines pointing outward from the source are called rays.

From the above figure, we can deduce that the $I=\frac{p_{\text{avg }}}{A}=\frac{p_{\text{avg }}}{4\pi r^2}$
So, from this equation, we can say that it varies inversely with the square of the distance.

Now, the appearance of sound to a human ear is characterized by -
a. Pitch
b. Loudness
c. quality

Pitch - The pitch of a sound is an attribute of the sound that tells us about its frequency. A sound that is at a high pitch, has a high frequency. And a sound at low pitch has a lower frequency.

Loudness -
The loudness that a person sense is related to the intensity of sound though it is not directly proportional to it. Loudness can be defined and represented as -

$\beta =10{\log }_{10}\left(\frac{I}{I_o}\right)$
 

Where I = Intensity of the sound

           I_o = Reference intensity (10^-12 W-m^-2)

For $\mathrm{I}={\mathrm{I}}_{\mathbf{0}}$, the sound level $\beta =0$