Sound Intensity Video Lessons

Concept

# Problem: 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/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 isβ=10log(I0)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 AWhat is the sound intensity level β, in decibels, of a sound wave whose intensity is 10 times the reference intensity (i.e., I=10I0)?Part BWhat is the sound intensity level β, in decibels, of a sound wave whose intensity is 100 times the reference intensity (i.e. I=100I0)?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=mI0).

###### FREE Expert Solution

Part A

Sound intensity level in decibels:

I = 10I0

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###### Problem Details

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/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(I0)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=10I0)?

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)?

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=mI0).