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?

Power, P = 20.4 kW

Explanation:

It is given that,

Intensity of sound,

Distance from the speakers, r = 25 m

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

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.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west