Question

The loudness l of a sound, measured in decibels, is given by l=10log10r, where r is the sound's relative intensity. suppose one person talks with a relative intensity of 10^6 or 60 decibels. how much louder would 100 people be, talking at the same intensity?

Answer 1

given,

I is the loudness of sound

I = 10 Log₁₀ r

r is relative intensity

at when relative intensity is 10⁶

I = 60 dB

how much louder when 100 people would be talking together

I = 10 Log₁₀ r

I = 10 Log₁₀ (10⁶ x 100)

I = 10 Log₁₀ (10⁸)

I = 80 dB

hence, the intensity will be increased by (80 dB -60 dB) 20 dB when 100 people start talking together.