12. A sound level of 96 dB is how many times as intense as one of 90 dB?

A sound level of 96 dB is 4 times as intense as one of 90 dB

Explanation:

The formula of the intensity level of sound in decibels is given as follows:

Intensity Level = 10 log₁₀(I/I₀)

where,

I = Intensity of Sound

I₀ = Reference Intensity Level = 10⁻¹² W/m²

Therefore, for 96 dB sound level:

96 = 10 log₁₀(I₁/10⁻¹²)

log₁₀(I₁/10⁻¹²) = 96/10

I₁/10⁻¹² = 10^9.6

I₁ = (10⁻¹²)(4 x 10⁹)

I₁ = 0.004 W/m²

For 90 dB sound level:

90 = 10 log₁₀(I₂/10⁻¹²)

log₁₀(I₂/10⁻¹²) = 90/10

I₂/10⁻¹² = 10^9

I₂ = (10⁻¹²)(10⁹)

I₂ = 0.001 W/m²

Therefore,

I₁/I₂ = 0.004/0.001

I₁ = 4 I₂

Hence, the sound level of 96 dB is 4 times as intense as one of 90 dB.