Intensity and Power - Talking

CONSIDER THIS:

You work at Science World, and an IMAX movie is about to start. You have to let the audience know about the rules of watching the movie in the globular theatre, which is

5 storeys (16.5m) high and has a diameter of 27m. The movie, producing a sound that is 80 dB loud, how much power would you require in order to talk over the movie?

CONSIDER THIS:

Understand that the speakers are arranged in a way that the entire audience hears 80 dB, but the maximum distance to the audience is 13.5m (due to the dome shape

of the theatre).

HINT 1: Use the relationship between dB and I to figure out the

sound intensity

0 dB = 10-12 W/m2

*remember I = I0 • 10β/10

HINT 2: Assuming that the power is being radiated uniformly in all directions

(isotropically), use the relationship between I and P

I = P/4πr2

SOLN: HINT 1: Use the relationship

between dB and I to figure out the sound intensity



80 db _____ 10 = 8



80 db _____ 10 = 8 108



80 db _____ 10 = 8 108

108 • 10-12



80 db _____ 10 = 8 108

108 • 10-12 = 10-4

SOLN: HINT 2: Assuming that the

power is being radiated uniformly in all directions





I = P/4πr2




I = P/4πr2

Rearrange the formula!




I = P/4πr2

I = P/4πr2

P = I • 4πr2




I = P/4πr2

I = P/4πr2

P = I • 4πr2 P = 10-4 • 4π(13.5)2

r = d/2 = 27/2 = 13.5

P = 10-4 • 2290.22

P = 0.229 W

THE END