A loudness L is given. Find the intensity of the sound.

Lequals=74.374.3 

dB

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Part 1

Iequals=enter your response here 

Upper W divided by m squaredW/m2 

​(Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to two decimal places as​ needed.)


To find the intensity of the sound \( I \), we can use the following formula that relates sound intensity to loudness in decibels (dB):

\[
L = 10 \log_{10}\left(\frac{I}{I_0}\right)
\]

Where:
- \( L \) is the loudness in decibels (dB).
- \( I \) is the intensity of the sound.
- \( I_0 \) is the reference intensity, typically \( I_0 = 1 \times 10^{-12} \, \text{W/m}^2 \) (the threshold of hearing).

We are given:
\[
L = 74.3 \, \text{dB}
\]

To solve for the intensity \( I \), we rearrange the formula:

\[
I = I_0 \times 10^{\frac{L}{10}}
\]

Now we can plug in the values:

\[
I = 1 \times 10^{-12} \times 10^{\frac{74.3}{10}}
\]

Let me calculate that for you.The intensity of the sound is approximately \( 2.69 \times 10^{-5} \, \text{W/m}^2 \).

Would you like further details or have any questions about this calculation?

Here are 5 related questions for further exploration:
1. How does the intensity of sound change with a 10 dB increase in loudness?
2. What is the intensity level of a sound that measures 60 dB?
3. How does distance affect the intensity of sound as perceived by a listener?
4. What is the loudness in decibels of a sound with intensity \( 1 \times 10^{-6} \, \text{W/m}^2 \)?
5. How does the logarithmic scale affect the perception of sound loudness?

**Tip:** A small increase in dB (like 10 dB) represents a significant change in intensity, often perceived as twice as loud!

A loudness L is given. Find the intensity of the sound. L = 74.3 dB. I = W/m^2 (Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to two decimal places as needed.)

Learn how to calculate the intensity of sound given a loudness of 74.3 dB using the logarithmic relationship between sound intensity and decibels. This problem involves logarithms, sound intensity formulas, and scientific notation. Suitable for students in Grades 10-12.

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