Question

A family ice show is held at an enclosed arena. The skaters perform to music playing at a level of 71.0 dB. This intensity level is too loud for your baby, who yells at 79.5 dB.

Answer 1

a) total sound intensity engulfs:

Sound intensity level in dB assigned to a sound of intensity I is defined as:
L = 10∙log₁₀( I/I₀ )
where I₀ = 10⁻¹²W/m² is the threshold of hearing
I = I₀ ∙ 10^( L/10) = 10^((L/10) - 12) W/m²

So
I_music = 10^((71/10) - 12) W/m² = 10^(-3.2)W/m² = 1.25×10^⁻5W/m²
I_baby = 10^((79.5/10) - 12) W/m² = 8.91×10⁻⁵W/m²
=>
I_total = I_music+ I_baby = 10.16×10^⁻5W/m²


(b) combined sound level

L_total = 10∙log₁₀( I_total/I₀ )
= 10∙log₁₀( 10.16×10^⁻5/10⁻¹² )
= 80.06dB