Question

Sound waves, measured in decibels (dB), are computed using the formula:f(x) = 10log I + 120, where I is the intensity of the sound measured in watts per square meter. What is the sound intensity for a dB reading of 100? Give your answer to the nearest hundredth of a sound intensity unit. Do not use commas or spaces in your answer. If your answer is 0.9 watts per square meter, then input only the 0.9. Do not input the units.

Answer 1

0.01

Explanation:

Sound waves, measured in decibels (dB), are computed using the formula:

`f(x)=10\log I+120`

I = the intensity of the sound measured in watts per square meter.

Given that the sound waves, f(x)=100, we want to find the value of I, the intensity of the sound.

Substitute f(x)=100 into the given formula:

`100=10\log I+120`

Then solve for I:

`\begin{gathered} \text{ Subtract 120 from both sides of the equation} \\ 100-120=10\log I+120-120 \\ -20=10\log I \\ \text{ Divide both sides by 10} \\ -(20)/(10)=(10\log I)/(10) \\ \log I=-2 \\ \text{ Change from logarithmic form to the exponential form} \\ I=10^(-2) \\ I=(1)/(10^2)=(1)/(100)=0.01\text{ watts per square meter} \end{gathered}`

The sound intensity for a dB reading of 100 is 0.01 watts per square meter.