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# The Decibel Scale (5 marks). The decibel scale is a logarithmic scale for measuring the sound...

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/m2 changes by a multiplicative factor. The number of decibels increases by 10 for a factor of 10 increase in intensity. a. What is the sound intensity level ??, in decibels, of a sound wave whose intensity is 10 times the reference intensity (i.e., ?? = 10??0)? Note that an intensity of ??0 corresponds to an intensity level of 0 dB. (1) b. What is the sound intensity level ??, in decibels, of a sound wave whose intensity is 100 times the reference intensity (i.e., ?? = 100??0)? (1) c. We often need to compute the change in decibels corresponding to a change in the intensity. Say a sound increases in intensity from ??1 to ??2. Take ?? to be the factor of increase of the intensity (i.e., ??2 = ????1). In other words, ?? = 2 would correspond to doubling the intensity, and so on. Calculate the change in decibels (???) corresponding to ?? = 2, ?? = 4, and ?? = 8. (3)

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