Mineral wool is a material used in construction for the purposes of insulation a

Question

Mineral wool is a material used in construction for the purposes of insulation and soundproofing. A sheet of 9 cm in thickness causes the original intensity to decrease to 65% of its original value.

You are trying to build a soundproof room that reduces sound coming in and out by 95%. That is, the intensity after crossing the walls is only 5% of the initial value.

In centimeters, and to two significant figures, what should be the thickness of the mineral wool used in the walls of your soundproof room?

Explanation / Answer

.65 .65^2 = .4225 .65^3 = 0.275 .65^4 = 0.1785 .65^5 = 0.116 .65^6 = 0.075 0.65^7 = 0.0490 only five percent remains so the thickness is 7*9cm = 63 cm if we wanted exact, we could say 0.65^6.955 = 0.048998 6.955*9 = 62.595, which is 63 cm to two sig figs.

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