# physics

A sheet of 6 cm in thickness causes the original intensity to decrease to 59% 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. What should be the thickness of the mineral wool used in the walls of your soundproof room?

This is the way I'm approaching this question, can someone confirm if it is the correct way, please? Thanks in advance.

I(i)= 1
I(f)= 1-0.59 = 0.41

ΔI = -βIΔz
0.41 = -β(1)(6)
β = -0.41/6

ΔI = -βIΔz
0.95 = -[-0.41/6](1)Δz
Δz = 0.95/(-[-0.41/6])

1. 👍 0
2. 👎 0
3. 👁 111
1. You modeled the intensity decrease as linear.
I think a more appropriate model is exponental decay.

I= Io e^(-kL) where k is some constant, L is distance.

.59=1 e^(-k6) then solve for k
ln .59= -6k
or k= (-ln .59)/6

solve for k. Then put it in the original equation

.95=e^(-kd) and solve for d.

1. 👍 0
2. 👎 0
2. Thank you!
That really helped. Now I'm getting an answer of 34 which seems reasonable, according to what the question is asking.

Also, if you don't mind answering, how would you know to use the exponential decay equation or the linear equation? Are there certain instances where it is better to use one over the other, and if so, how can you know this?

1. 👍 0
2. 👎 0
posted by dawn
3. Experience. Most oscillations dampen in physical systems exponentially. The reason is because the amount of energy lost in the media is proportional to the amount of energy in the wave. In differential equations (adv calculus), you recognize immediately this leads to exponential decay.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### physics

Mineral wool is a material used in construction for the purposes of insulation and soundproofing. A sheet of 11 cm in thickness causes the original intensity to decrease to 63% of its original value. You are trying to build a

2. ### College Alg

The intensity I of an x-ray after it has passed through a material that is x centimeters thick is given by I = I0e^–kx, where I0 is the initial intensity of the x-ray and k is a number that depends on the material. The constant

asked by Dale on November 6, 2016
3. ### math

help A paper sheet of 0.1 mm thickness is taken. Is cut in two and placed one above the other; is a thickness of 0.2 mm. This roll is cut into two and put prte above the other; is a thickness of 0.4 mm. The next time the same

asked by Myke on July 14, 2014
4. ### physics

A copper sheet of thickness 2.09 mm is bonded to a steel sheet of thickness 1.35 mm. The outside surface of the copper sheet is held at a temperature of 100.0°C and the steel sheet at 26.3°C a) Determine the temperature (in °C)

asked by maria on December 9, 2011

A copper sheet of thickness 2.09 mm is bonded to a steel sheet of thickness 1.35 mm. The outside surface of the copper sheet is held at a temperature of 100.0°C and the steel sheet at 26.3°C. a) Determine the temperature (in

asked by maria on December 10, 2011
6. ### physic

A copper sheet of thickness 2.01 mm is bonded to a steel sheet of thickness 1.07 mm. The outside surface of the copper sheet is held at a temperature of 100.0°C and the steel sheet at 22.9°C. a) Determine the temperature (in

7. ### university physics

A copper sheet of thickness 2.19 mm is bonded to a steel sheet of thickness 1.13 mm. The outside surface of the copper sheet is held at a temperature of 100.0°C and the steel sheet at 25.7°C. a) Determine the temperature (in

asked by jane on December 4, 2012
8. ### Physics

A copper sheet of thickness 2.49 mm is bonded to a steel sheet of thickness 1.51 mm. The outside surface of the copper sheet is held at a temperature of 100.0°C and the steel sheet at 24.1°C. a) Determine the temperature (in

asked by Lyra on January 28, 2014
9. ### physics

A copper sheet of thickness 2.13 mm is bonded to a steel sheet of thickness 1.41 mm. The outside surface of the copper sheet is held at a temperature of 100.0°C and the steel sheet at 24.3°C. a) Determine the temperature (in

asked by Anonymous on November 5, 2014
10. ### Applied maths

2. When light passes through a transparent medium, its intensity I at a depth d can be modelled using the equation where I0 is the initial intensity, and k is a constant. If the intensity of sunlight is reduced to 54% of its

asked by DAVID on February 13, 2013

More Similar Questions