The toadfish makes use of resonance in a closed tube to produce very loud sounds. The tube is its swim bladder, used as an amplifier. The sound level of this creature has been measured as high as 100 dB. (a) Calculate the intensity of the sound wave emitted. W/m2 (b) What is the intensity level if three of these toadfish try to make a sound at the same time

a)     I = 10⁻² W / m², b)   β = 104.8 db

Explanation:

a) For this exercise we use the definition of decibels

           β = 10 log

where I and Io are the intensities produced and the sound threshold

I₀ = 10⁻¹² W / m²

            log \frac{I}{I_o} =   β / 10

            I = Io

let's calculate

            I = 10⁻¹²  

            I = 10⁻² W / m²

b) each toad produces the same sound for which the total intensity is

            I_total = 3 I

            I_total = 3 10⁻² W / m²

expressed in decibels

           β = 10 log ()

           β = 104.8 db