First slide

Intensity of

Question

A point source of power 50 $π$ watts is producing sound waves of frequency 1875 Hz. The velocity of sound is 330m/s, atmospheric pressure is $1.0 \times 10^{5} {Nm}^{- 2}$ , density of air is 1.0 kg $m^{- 3}$ . Then pressure amplitude at , $r = \sqrt{330} m$ from the point source is (using $π$ = $\frac{22}{7}$ ):

Moderate

A

5 ${Nm}^{- 2}$
B

10 ${Nm}^{- 2}$
C

15 ${Nm}^{- 2}$
D

20 ${Nm}^{- 2}$

Solution

$I = \frac{P_{0}^{2}}{2 ρV} \Rightarrow \frac{P}{4 {πr}^{2}} = \frac{P_{0}^{2}}{2 ρV}; where P, P_{0}, V are power, pressure amplitude and velocity respectivley$
$\Rightarrow P_{0} = \sqrt{\frac{PρV}{2 {πr}^{2}}} = \sqrt{\frac{50 π \times 1 \times 330}{2 π \times 330}} = 5$ N/m²

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