Problem 57-4
Source: Problem elaborated by the author of the site.
Supondo um alto-falante como uma fonte emissora puntual e esteja emitindo uma
potência de 10 W, calcule a pressão sonora a 1 metro e a 10 metros
de distância do mesmo.
Solution of the Problem 57-4
As the speaker is being considered a point source it means that it emits
sound waves with equal intensity in all directions of space. So we must calculate
the surface area of a sphere where the center of the sphere is the speaker. The area
of the surface of a sphere is given by A1 = 4 π r2. Then,
for 1 meter:
For the distance of 10 meters:
The equation for calculating the signal intensity is given by I = P / A. Then, for the distance of 1 meter:
For the distance of 10 meters:
To calculate the sound pressure, remember that the reference level of the sound intensity is
Io = 10-12 W / m2 and the equation to be used is:
Then, for the distance of 1 meter:
And for the distance of 10 meters:
Note that even for a distance of 10 meters, the sound pressure level is very high and
can cause serious damage to human hearing, since the limit considered
sure is the level of 85 dB.
Note that the power of 10 W emitted by the speaker is acoustic power.
It is not the electrical power delivered to the speaker. Consider that a speaker
It has an efficiency, on average, of 4%. Thus, for a speaker to emit
10 W of acoustic power requires approximately 250 W of electrical power from the amplifier.
This is because most of the energy supplied to the speaker is converted into heat,
and only a small fraction is transformed into sound.
