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. The general formula for the sound intensity level, in decibels, corresponding to intensity I is β=10log(II0)dB where I0 is a reference intensity. For sound waves, I0 is taken to be 10−12W/m2. 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 i0)? 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=100i0)? 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=mI0). Part C Calculate the change in decibels ( Δβ2, Δβ4, and Δβ8) corresponding to m=2, m=4, and m=8. (to the nearest integer--this will give an accuracy of 20%, which is good enough for sound)
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. The general formula for the sound intensity level, in decibels, corresponding to intensity I is β=10log(II0)dB
where I0 is a reference intensity. For sound waves, I0 is taken to be 10−12W/m2. 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 i0)?
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=100i0)?
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=mI0).
Part C
Calculate the change in decibels ( Δβ2, Δβ4, and Δβ8) corresponding to m=2, m=4, and m=8. (to the nearest integer--this will give an accuracy of 20%, which is good enough for sound)
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