Question

An amplifier produces a sound wave with a power of 1.00 μW (micro-Watt). If it is a point source and radiates uniformly in all directions, (a) what is the intensity at a point 3m away? (b) What is the sound level in dB at the same point (3m away from the source)?

Answer 1

Answer:

(a) $I=8.84*10^{-9}W/m^{2}$

(b) $\beta =39.46dB$

Explanation:

Given data

The source is 1.00 μW

The point is 3m away from the point source

For Part (a)

The intensity at a certain distance from a point source that emits sound wave is given as:

$I=\frac{P_{s} }{4\pi r^{2} }\\I=\frac{1*10^{-6}W }{4\pi (3m)^{2} } \\I=8.84*10^{-9}W/m^{2}$

For Part (b)

The Sound level is given by

β=(10dB)×log(I/I₀)

Where

I₀=1×10⁻¹²W/m²

Substitute the given values to find Sound level

So

$\beta =(10dB)log(\frac{8.84*10^{-9}W/m^{2} }{1*10^{-12}W/m^{2}} )\\\beta =39.46dB$