Suppose that a siren makes a sound reaching 120 decibels, but a wolf’s howl only reaches 90 decibels. 120 dB is how many times louder than 90 dB? 1000 times

I₁/I₂ = 1000

Thus, the sound of siren is 1000 times louder than the sound of wolf's howl.

Explanation:

First, we need to calculate the intensity of both the sounds. The formula for sound level is given as:

L = 10 log[I/I₀]

where,

L = Sound Level in dB

I = Intensity of sound

I₀ = Reference intensity = 10⁻¹² W/m²

FOR SOUND OF SIREN:

L = 120 dB

I = I₁ = ?

Therefore,

120 = 10 log[I₁/10⁻¹²]

log[I₁/10⁻¹²] = (120)/10

log[I₁/10⁻¹²] = 12

I₁/10⁻¹² = 10¹²

I₁ = (10¹²)(10⁻¹²)

I₁ = 1

FOR SOUND OF WOLF'S HOWL:

L = 90 dB

I = I₂ = ?

Therefore,

90 = 10 log[I₂/10⁻¹²]

log[I₂/10⁻¹²] = (90)/10

log[I₂/10⁻¹²] = 9

I₂/10⁻¹² = 10⁹

I₂ = (10⁹)(10⁻¹²)

I₂ = 10⁻³

Now, we divide the intensities:

I₁/I₂ = 1/10⁻³

I₁/I₂ = 10³

I₁/I₂ = 1000

Thus, the sound of siren is 1000 times louder than the sound of wolf's howl.

trig 15.3 cos