30 seconds of exposure to 115 db sound can damage your hearing, but a much quieter 94 db may begin to cause damage after 1 hour of continuous exposure. you are going to an outdoor concert, and you'll be standing near a speaker that emits 50 w of acoustic power as a spherical wave. what minimum distance should you be from the speaker to keep the sound intensity level below 94 db?

39.8 m ≈ 40 m

Explanation:

power (P) = 50 W

sound intensity level () = 94 dB

the distance (r) can be gotten from the equation I = (take not that π is shown as )

making r the subject of the formula we have r =   (take not that π is shown as )

But to apply this equation we need to get the value of the intensity (I)

now that we have the value of the intensity (I)  we can substitute it into the formula for the distance (r)

distance (r) =

r = = 39.8 m ≈ 40 m

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft