Question

engine emits sound uniformly in all directions, radiating an acoustic power of 3.65 × 10 5 W. 3.65×105 W. Find the intensity of the sound at a distance of 52.7 m 52.7 m from

Answer 1

Answer:

10.46W/m²

Explanation:

The intensity (I) of a sound is related to the power (P) radiated by the sound within an area (A) as follows;

I = $\frac{P}{A}$              ----------------(i)

But;

A = 4$\pi$ r²

Where;

r is the specified distance covered by the sound.

Substitute A = 4 $\pi$ r² into equation (i) to get;

I = $\frac{P}{4\pi r^{2} }$               ------------------------(ii)

From the question;

P = acoustic power = 3.65 x 10⁵W

r = 52.7m

To calculate the intensity of the sound, take $\pi$ = 3.142 and substitute other values into equation (ii) as follows;

I = $\frac{3.65*10^5}{4*3.142*52.7^2}$

I = $\frac{3.65*10^5}{34904.98}$

I = 10.46W/m²

Therefore, the intensity of the sound at that distance is 10.46W/m²

Answer 2

Answer:

130.2dB

Explanation:

The formula for determining the intensity of a wave is expressed as

$I=\frac{P}{A}$

Where P is the power in watts, and A is the area of the sphere formed by the wave

Data given

Power,P=3.65*10^5W

distance,d=52.7

Hence since the distance represent the radius, we can determine the area of the sphere formed

$A=4\pi r^{2}\\A=4\pi *52.7^{2}\\A=34900.45m^2$

The intensity can be computed as

$I=\frac{3.65*10^5}{34900.45}\\ I=10.46W/m^2$

we can convert to decibel

$I=10log\frac{10.46}{10^{-12}} \\I=130.2dB$