Question

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

• A. $5\, Nm ^{-2}$
• B. $10\, Nm ^{-2}$
• C. $15\, Nm ^{-2}$
• D. $20\, Nm ^{-2}$

Answer 1

Answer: (A)

$I=\frac{P_{0}^{2}}{2 \rho V}$
$\Rightarrow \frac{P}{4 \pi r^{2}}$
$=\frac{P_{0}^{2}}{2 \rho V} ;$ where $P, P_{0}, V$ are power,
pressure amplitude and velocity respectively.
$\Rightarrow P_{0}=\sqrt{\frac{P \rho V}{2 \pi r^{2}}}$
$=\sqrt{\frac{50 \pi \times 1 \times 330}{2 \pi \times 330}}=5$