You own a Sprite bottling factory with 640 machines. An inspector observes your

Question

You own a Sprite bottling factory with 640 machines. An inspector observes your factory and mandates that you must decrease your sound decibel level from the current value of 84dB down to 68dB. Assuming you can only remove machines (a) What is the intensity of one bottling machine? (b) What is the intensity level (decibels) of one bottling machine? (c) How many machines do you need to remove from the premises? (d) Your new manager is proud of himself. He sold some of your machines to a Pepsi bottler and reduced the decibel level to 62dB. How many machines do you have left?

Explanation / Answer

Here ,

let the sound intensity level of a machine is s1

as sound level = s1 + 10 * log(640)

84 = s1 + 28.06

s1 = 55.93 dB

10 * log(I/Io) = 55.93

log(I/(1 *10^-12)) = 5.593

I = 3.92 *10^-7 W/m^2

the intensity of each machine is 3.92 *10^-7 W/m^2

b)

intensity level of a single machine =s1

intensity level of a single machine = 55.93 dB

c)

for sound level = 68 dB

68 = 55.93 + 10 * log(N)

N = 16.1

machines removed = 640 - 16

machines removed = 624

the machines removed is 624

d)

for sound level = 62 dB

62 = 55.93 + 10 * log(N)

N = 4

the number of machines left is 4

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