Question

How much more intense is a sound of 70 dB than a sound of 20 dB ?

Answer 1

Sound Intensity level is given by:

SL = 10*log (I/I0)

I0 = Human threshold intensity = 10^-12 W/m^2

for 70 dB sound:

SL1 = 70 dB = 10*log (I1/I0)

log (I1/10^-12) = 70/10

I1/10^-12 = 10^7

I1 = 10^7*10^-12 = 10^-5 W/m^2

for 20 dB sound:

SL2 = 20 dB = 10*log (I2/I0)

log (I2/10^-12) = 20/10

I2/10^-12 = 10^2

I2 = 10^2*10^-12 = 10^-10 W/m^2

So I1/I2 = 10^-5/10^-10

I1/I2 = 10^5

I1 = 10^5*I2

So 70 dB is 10^5 times more intense than 20 dB

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