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.

A. What is the sound intensity level β, in decibels, of a sound wave whose intensity is 10 times the reference intensity?

B. What is the sound intensity level β, in decibels, of a sound wave whose intensity is 100 times the reference intensity?

Note: Complete Question:

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=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.

Concepts and reason

The concept required to solve this problem is decibel scale of sound intensity.

Use the formula of sound intensity level in decibels and substitute the value of intensity to calculate decibels for all the parts.

Find the given 2 attachments for complete solution. Thanks

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