Use the fact that the loudness of sound in decibels perceive

Use the fact that the loudness of sound (in decibels) perceived by the human ear depends on intensity levels according to

L = 10 log(I/I₀)

where I₀ is the threshold of hearing for the average human ear.

Find the loudness when I is 10,000 times I₀. This is the intensity level of the average voice.

L=

Solution

Given loudness L = 10 log(I/I0)

where L-Loudness

I-Intensity of sound

I0- Threshold of hearing for the average human ear.

Need to find the loudness when I is 10,000 times I0.

I=10,000 * I0

L = 10 log(I/I0)

= 10 log((10,000 * I0)/I0)

= 10 log(10,000)

= 10 log(10⁴)

= 10 * 4 log(10)

= 40 log(10)

= 40 (log10=1)

L=40 decibles

Therefore loudness when I is 10,000 times I0 is 40 decibles.