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At a rock concert, it is desired to have a sound intensity of 2.6 W/m2 for those patrons seated 25 m from the speakers. If you assume that the sound is emitted from the speakers equally in all directions, what is the power output needed from the sound system?

Respuesta :

Answer:

Power, P = 20.4 kW

Explanation:

It is given that,

Intensity of sound, [tex]I=2.6\ W/m^2[/tex]

Distance from the speakers, r = 25 m

We need to find the power output needed from the sound system. Intensity is given by :

[tex]I=\dfrac{P}{A}[/tex]

[tex]P=I\times 4 \pi r^2[/tex]

[tex]P=2.6\times 4\pi \times (25)^2[/tex]

P = 20420.35 Watts

or

P = 20.4 kW

So, the power output needed from the sound system is 20.4 kW. Hence, this is the required solution.