A weather emergency siren is mounted on a tower, 105 m above the ground. On one hand, it would be a good idea to make the siren very loud so that it will warn as many people as possible. On the other hand, safety regulations prohibit the siren from exceeding an intensity level of 101 dB for workers standing on the ground directly below the siren. Assuming that the sound is uniformly emitted, what is the maximum power that the siren can put out

Explanation:

101 dB = 10.1 B.

Maximum intensity of sound allowed = 10.1 B

Intensity of sound in terms of W/m² can be found as follows

log (I / I₀) = 10.1

I / I₀ = 10¹⁰°¹

I = I₀ X 10¹⁰°¹

= 10⁻¹² X  10¹⁰°¹

= 10⁻¹°⁹ W/m²

105 m above the ground the this intensity will be 105² times

intensity at source point = 10⁻¹°⁹ x 105²

= 138.79 W/m²

energy of sound from source

= 4π times

= 4 x 3.14 x 138.79

= 1743.28W/m²

To calculate in terms of decibel :

log 1743.28 / 10⁻¹²

= log 1743.28 +12

= 15.24 B

= 152.4 dB .

152.4 dB .

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.