Question

The sound from a trumpet radiates uniformly in all directions in air with a temperature of 20∘C. At a distance of 5.18 m from the trumpet the sound intensity level is 54.0 dB . The frequency is 561 Hz .

What is the pressure amplitude at this distance?

Answer 1

Answer:

$P=1.44*10^{-2}Pa$

Explanation:

The pressure amplitude is given by:

$P=\sqrt{2I\rho v$

Here, I is the sound intensity, $\rho$ the density of the air and v the speed of air.

The sound intensity can be calculated from:

$I=10^\beta I_0$

Where $\beta$ is the sound intensity level in bels and $I_0$ is the reference sound intensity. So, replacing (2) in (1):

$P=\sqrt{2(10^\beta) I_o \rho v}\\P=\sqrt{2(10^{5.4})(10^{-14}\frac{W}{m^2})(1.2\frac{kg}{m^3})(344\frac{m}{s})}\\P=1.44*10^{-2}Pa$