Question

A source of sound operates at 2.0 kHz, 20 W emitting sound uniformly in all directions. The speed of sound in air is 340 m s and the density of air is $1.2kg{m}^{-3}$. (a) What is the intensity at a distance of 6.0 m from the source ? (b) What will be the pressure amplitude at this point ? (c) What will be the displacement amplitude at this point ?

Answer 1

Here given, $V_{air}=340m/s$

power $=\frac{e}{t}=20W$

f=2,000 Hz, $p=1.2kg/m^3$

So, Intensity,

$I=\frac{e}{t.A}=\frac{20}{4\pi r^2}=\frac{20}{4\times \pi \times 6^2}$

$=44mw/m^2$ [because r =8 m]

(b)We know that,

$I=\frac{p_0^2}{2p{V}_{air}}$

$\Rightarrow P_0=\sqrt{1\times 2p{V}_{air}}$

$=\sqrt{2\times 12\times 340\times 44\times {10}^{-3}}$

$=6.0N/m^2$

(c)We know that,

$I=2{\pi }^2{S}_0^2{v}^{2}pV$

where $S_0$ =displacement amplitude

$\Rightarrow S_0=\sqrt{\frac{I}{2{\pi }^2{p}^{2}p{V}_{air}}}$

Putting the value we get,

$S_0=1.2\times {10}^{-6}m$