Question

The intensity levels of two people's speech are 60.0 dB and 64.5 dB, respectively. What is the intensity level of the combined sounds? (in dB)

Answer 1

Solution:

for Sound Intensity level: L₁ = 60 dB

Since: L = 10 log(I/Io)

Thus : 60 = 10 log(I₁/I_o)

6.0 = log (I₁/I_o)

I₁ / I_o = 10 ^6.0

I₁ = 10 ^6.0 I_o = 10 ^6.0 x 10 ^-12 = 10 ^-6 W/m ² = 1 x 10 ^-6 W/m ²

Similarly:

for Sound Intensity level : L₂ = 64.5 dB

Thus : 64.5 = 10 log(I₂/I_o)

6.45 = log (I₂/I_o)

I₂ / I_o = 10 ^6.45

I₂ = 10 ^6.45 I_o = 10 ^6.45 x 10 ^-12 = 10 ^-5.55 W/m ² = 2.8184 x 10 ^-6 W/m ²

Therefore: Combined intensity: I = I₁ + I₂ = 3.8184 x10^-6 W/m ²

the intensity level of the combined sounds: L = 10 log(I/ Io)

L = 10 log [( 3.8184 x 10 ^-6 )/(10 ^-12 ) ] = 65.82 dB