**Part A**

Sound intensity level in decibels:

I = 10I_{0}

To understand the decibel scale.

The decibel scale is a logarithmic scale for measuring the sound intensity level. Because the decibel scale is logarithmic, it changes by an additive constant when the intensity as measured in W/m^{2} changes by a multiplicative factor. The number of decibels increases by 10 for a factor of 10 increase in intensity. The general formula for the sound intensity level, in decibels, corresponding to intensity *I* is

*β*=10log(*I*_{0})dB,

where *I*_{0} is a reference intensity. For sound waves, *I*_{0} is taken to be 10^{−12}W/m^{2}. Note that log refers to the logarithm to the base 10.

**Part A**

What is the sound intensity level *β*, in decibels, of a sound wave whose intensity is 10 times the reference intensity (i.e., *I*=10*I*_{0})?

**Part B**

What is the sound intensity level *β*, in decibels, of a sound wave whose intensity is 100 times the reference intensity (i.e. *I*=100*I*_{0})?

Express the sound intensity numerically to the nearest integer.

One often needs to compute the change in decibels corresponding to a change in the physical intensity measured in units of power per unit area. Take *m* to be the factor of increase of the physical intensity (i.e., *I*=*m**I*_{0}).

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