Question

A rock band's music has an average sound level of 147 dB. (a) What would the average level be if the intensity was reduced by 1/2? (b) What would the average level be if the intensity was reduced by 1/100? (c) What would the average level be if the intensity was doubled? (d) What would the average level be if the intensity was increased to 10 times the original value?

Answer 1

intensity level B = 10 dB log(I/Io)

Io is constant = 10^-12 W/m^2

I is intensity

now if I = I/2

so 147 = 10 dB log(I/Io)

log (I/Io) - 147/10 = 14.7

I/Io = 10^14.7

I = 10^14.7 *10^-12

I = 501.18 W/m^2

no if I = I/2 = 501.18/2 = 250.59 W/m^2

leve B = 10dB log(250.59/10^-12)

level B = 144 dB

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part B:

I/100 = 501.18/100 = 5.01 W/m^2

level B = 10 dB log(5.01*10^12)

B = 127 dB

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part C:

if I = 2* 501.18 = 1002.36 W/m^2

level B = 10 dB log(1002.36*10^12)

B = 150 dB

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part D :

If I = 501.18*10 = 5011.8 W/m^2

so

level B = 10 dB log(5011.8*10^12)

B = 157 dB