Loudspeaaaakerrrrr and sound waves!!!?

Question

An outside loudspeaker (considered a small source) emits sound waves with a power output of 120 W.
(a) Find the intensity 10.5 m from the source.
_________ W/m2
(b) Find the intensity level in decibels at that distance.
_________dB
(c) At what distance would you experience the sound at the threshold of pain, 120 dB?
__________ m

Answer 1

Intensity is watt/m^2. At a distance of 10.5 meters from the source, the 120W of power is spread over an area of 4π*(10.5^2) sq. meters (the surface area of a sphere of radius 10.5 m), so the intensity is

I = 120 / 4π*(10.5^2) watt/m^2 = 0.087 watt/m^2

In decibels, this would be 10*log(I/I0). I is what you have above, I0 is 10^-12 watt/m^2 I = 109.4db

For I to be 120db, that means 120 = 10*log(I/I0), or 12 = log(I/I0)), I/I0 = 10^12, I = I0*10^12 = 1.

120/4*π^r^2 = 1, r = √[30/π] meters = 3.09m

Answer 2

first you have some items not correct. if you specify the outputof a loudspeaker it's in SPL, not watts. plus you must specify the measurement distance as inverse square law holds true in this application. this is probably considered a "single point source". so you might want to chk that.you'll need to specify that your Wm2 are acoustical watts (a bit different than electrical watts). The threshold of pain...well that actuallywill varie with people. 180 dB is = to one atmosphere or circa 14 lbs/in2. in your (b) in order to calculate this number you must know the sensitivity of the driver (not given). then convert that to power in space ...re. acoustical watts. i'm thinking all the required parts are not listed here in your question. fix that and repost and i'll see what i can do. i answer these questions all the time for relaxation