Question

By what factor is the intensity of sound at a rock concert louder than that of a whisper when the two intensity levels are 120 dB and 21 dB, respectively? c) 6.50x1010 a) 3.16x1010 d) 7.94x100 b) 1.58x1010 e) 3.98x109

Answer 1

d)
`7.94* 10^(9)`

Step-by-step explanation:

β₁ = sound level of sound at rock concert = 120 dB

β₂ = sound level of sound due to whisper = 21 dB

I₁ = Intensity of sound at rock concert

I₂ = Intensity of sound due to whisper

sound level of sound at rock concert is given as

`\beta _(1) = 10 log\left ( (I_(1))/(10^(-12)) \right )`

`120 = 10 log\left ( (I_(1))/(10^(-12)) \right )`

`12 = log\left ( (I_(1))/(10^(-12)) \right )` Eq-1

sound level due to whisper is given as

`\beta _(2) = 10 log\left ( (I_(2))/(10^(-12)) \right )`

`21 = 10 log\left ( (I_(2))/(10^(-12)) \right )`

`2.1 = log\left ( (I_(2))/(10^(-12)) \right )` Eq-2

subtracting Eq-2 from Eq-1

`12 - 2.1 = log\left ( (I_(1))/(10^(-12)) \right ) - log\left ( (I_(2))/(10^(-12)) \right )`

`9.9 = log\left ( (I_(1))/(I_(2)) \right )`

`\left ( (I_(1))/(I_(2)) \right ) = 7.94* 10^(9)`