### Sound Intensity and Decibel LevelsYou are in a room where there are two machines. One creates a sound level of 80 dB; and the other 90 dB as perceived by your ears.#### Questions:a. What is the sound intensity in W/m² created by machine 1? b. What is the sound intensity in W/m² created by machine 2? c. Determine the total sound level in dB you experience in that room.Fig. 1: [Diagram/graph not included in the image for this problem]**Explanation:**1. **Sound Intensity and Decibels:** - **Decibel (dB)** is a logarithmic unit used to measure sound level. It quantifies sound intensity relative to a reference level. - **Sound Intensity (I)** in W/m² is a measure of the power per unit area carried by a sound wave.2. **Formulas:** - Sound Level (L) in dB: \[ L = 10 \cdot \log_{10} \left( \frac{I}{I_0} \right) \] where \( I_0 = 10^{-12} \, \text{W/m}^2 \) is the reference intensity. - To find the intensity \( I \) for a given sound level: \[ I = I_0 \cdot 10^{\frac{L}{10}} \] 3. **Calculations:** - For machine 1 (80 dB): \[ I_1 = 10^{-12} \cdot 10^{\frac{80}{10}} = 10^{-12} \cdot 10^8 = 10^{-4} \, \text{W/m}^2 \] - For machine 2 (90 dB): \[ I_2 = 10^{-12} \cdot 10^{\frac{90}{10}} = 10^{-12} \cdot 10^9 = 10^{-3} \, \text{W/m}^2 \] - To find the total sound level: - Combine the intensities: \[ I_{\text{total}} = I_1 + I_2 = 10^{-4} + 10^{-3

We have:The sound level created by the machine 1 is The sound level created by the machine 2 is The…

You are in a room where there are two machines. One creates a sound level of 80 dB; and the other 90 dB as perceived by your ears. a. What is the sound intensity in W/m2 created by machine 1? b. What is the sound intensity in W/m2 created by machine 2? c. Determine the total sound level in dB you experience in that room.

You are in a room where there are two machines. One creates a sound level of 80 dB; and the other 90 dB as perceived by your ears. a. What is the sound intensity in W/m2 created by machine 1? b. What is the sound intensity in W/m2 created by machine 2? c. Determine the total sound level in dB you experience in that room.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

### Sound Intensity and Decibel Levels

You are in a room where there are two machines. One creates a sound level of 80 dB; and the other 90 dB as perceived by your ears.

#### Questions:
a. What is the sound intensity in W/m² created by machine 1?
b. What is the sound intensity in W/m² created by machine 2?
c. Determine the total sound level in dB you experience in that room.

Fig. 1: [Diagram/graph not included in the image for this problem]

**Explanation:**

1. **Sound Intensity and Decibels:**
- **Decibel (dB)** is a logarithmic unit used to measure sound level. It quantifies sound intensity relative to a reference level.
- **Sound Intensity (I)** in W/m² is a measure of the power per unit area carried by a sound wave.

2. **Formulas:**
- Sound Level (L) in dB:
\[ L = 10 \cdot \log_{10} \left( \frac{I}{I_0} \right) \]
where \( I_0 = 10^{-12} \, \text{W/m}^2 \) is the reference intensity.

- To find the intensity \( I \) for a given sound level:
\[ I = I_0 \cdot 10^{\frac{L}{10}} \]

3. **Calculations:**
- For machine 1 (80 dB):
\[ I_1 = 10^{-12} \cdot 10^{\frac{80}{10}} = 10^{-12} \cdot 10^8 = 10^{-4} \, \text{W/m}^2 \]

- For machine 2 (90 dB):
\[ I_2 = 10^{-12} \cdot 10^{\frac{90}{10}} = 10^{-12} \cdot 10^9 = 10^{-3} \, \text{W/m}^2 \]

- To find the total sound level:
- Combine the intensities:
\[ I_{\text{total}} = I_1 + I_2 = 10^{-4} + 10^{-3

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