The intensity of a sound in units of dB is given by \displaystyle I(\text{dB})=10\log\left(\frac{I}{I_0}\right)where  and  are measured in units of W m-2 and the value of  is 10-12 W m-2.

The sound intensity of a particular brand of washing machine is  dB. 

What is the sound intensity  in W m-2?

Give your answer to 2 significant figures.

N.B. You may wish to input your answer in scientific notation. For example, to input a value of  you would enter 3.4 * 10 ^ -5 in the input box.

The intensity of a sound in decibels is given by the equation:

\[
I(\text{dB}) = 10 \log\left(\frac{I}{I_0}\right)
\]

where:
- \( I \) is the sound intensity in \( \text{W/m}^2 \),
- \( I_0 = 10^{-12} \, \text{W/m}^2 \) is the reference sound intensity.

To find the intensity \( I \) from the decibel value \( I(\text{dB}) \), we can rearrange the formula as follows:

1. Start with the given equation:
\[
I(\text{dB}) = 10 \log\left(\frac{I}{I_0}\right)
\]
2. Divide both sides by 10:
\[
\frac{I(\text{dB})}{10} = \log\left(\frac{I}{I_0}\right)
\]
3. Convert the logarithmic equation to its exponential form:
\[
\frac{I}{I_0} = 10^{\frac{I(\text{dB})}{10}}
\]
4. Multiply both sides by \( I_0 \) to isolate \( I \):
\[
I = I_0 \cdot 10^{\frac{I(\text{dB})}{10}}
\]

Now, substitute \( I_0 = 10^{-12} \, \text{W/m}^2 \) and the given decibel value for the washing machine (let's call this value \( I(\text{dB}) \)):

\[
I = 10^{-12} \cdot 10^{\frac{I(\text{dB})}{10}}
\]

Please provide the value of \( I(\text{dB}) \) so I can calculate the intensity in \( \text{W/m}^2 \).

The intensity of a sound in units of dB is given by I(dB) = 10 log(I / I_0), where I and I_0 are measured in units of W m^-2, and the value of I_0 is 10^-12 W m^-2. The sound intensity of a particular brand of washing machine is dB. What is the sound intensity I in W m^-2? Give your answer to 2 significant figures.

Learn how to calculate sound intensity in W/m^2 from decibel values using logarithmic equations. This problem explains the formula I(dB) = 10 log(I / I_0), converting sound decibels to intensity for a washing machine. Suitable for high school students in Grades 10-12.

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