The decibel (dB) is a logarithmic unit that indicates the ratio of a physical qu

Question

The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities. A decibel is one tenth of a bel, a seldom-used unit . The Intensity Level (IL) in decibels is equal to 10 times the log of the ratio of the actual sound intensity (W/m^2) to a minimum standard intensity of 1x10^-12 W/m2})

PART B: The decibel level of a sound source at a distance of 1 m is equal to 65 decibels. Find the sound intensity in watts per meter squared, for this sound source at one meter.

Explanation / Answer

40dB=10dBlog10(I/I0)

log10(I/I0)=4

I/I0=10^4

I=10^-12*10^4=10^-8W/m^2

now the intensity of 4 such sound sources is I1 =4*10^-8W/m^2

so sound intensity in decibel =10dBlog10 (I1/I0)

=10dBlog10 (4*10^-8/10^-12)

=10dBlog10 (4*10^4)

=10dB(log10 4+log10 10^4)=10dB(log10 4+4)=10dB(0.602+4)=46.02dB

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