The sound level at a distance d=34 m from a loudspeaker is 70 dB. What is the power (in Watt) at which sound energy is being produced by the loudspeaker?. The threshold of hearing, lo = 1*10-12 W/m2, %3D A. 0.5265 B.O.3812 C. 0.1453 D. None

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**Sound Level Calculation**

The sound level at a distance \( d = 34 \) meters from a loudspeaker is 70 dB. What is the power (in Watt) at which sound energy is being produced by the loudspeaker? The threshold of hearing, \( I_0 = 1 \times 10^{-12} \) \(W/m^2\).

**Options:**

- A. 0.5265
- B. 0.3812
- C. 0.1453
- D. None
- E. 0.5812

To determine the correct answer, students need to use the following formula and steps:

1. **Sound Intensity Level Formula:**
   \[
   L = 10 \log \left( \frac{I}{I_0} \right)
   \]
   Where \( L \) is the sound level in decibels (dB), \( I \) is the sound intensity, and \( I_0 \) is the reference sound intensity (threshold of hearing).

2. **Rearrange to Find Intensity (I):**
   \[
   \frac{L}{10} = \log \left( \frac{I}{I_0} \right)
   \]
   \[
   10^{\frac{L}{10}} = \frac{I}{I_0}
   \]
   \[
   I = I_0 \times 10^{\frac{L}{10}}
   \]

3. **Calculate the Sound Intensity:**
   \[
   I = 1 \times 10^{-12} \, W/m^2 \times 10^{\frac{70}{10}}
   \]
   \[
   I = 1 \times 10^{-12} \, W/m^2 \times 10^7
   \]
   \[
   I = 1 \times 10^{-5} \, W/m^2
   \]

4. **Relation Between Intensity and Power:**
   \[
   I = \frac{P}{A}
   \]
   Here, \( P \) is the power and \( A \) is the surface area of a sphere with radius \( r = d \):
   \[
   A = 4 \pi d^2
   \]
   Hence,
   \[
Transcribed Image Text:**Sound Level Calculation** The sound level at a distance \( d = 34 \) meters from a loudspeaker is 70 dB. What is the power (in Watt) at which sound energy is being produced by the loudspeaker? The threshold of hearing, \( I_0 = 1 \times 10^{-12} \) \(W/m^2\). **Options:** - A. 0.5265 - B. 0.3812 - C. 0.1453 - D. None - E. 0.5812 To determine the correct answer, students need to use the following formula and steps: 1. **Sound Intensity Level Formula:** \[ L = 10 \log \left( \frac{I}{I_0} \right) \] Where \( L \) is the sound level in decibels (dB), \( I \) is the sound intensity, and \( I_0 \) is the reference sound intensity (threshold of hearing). 2. **Rearrange to Find Intensity (I):** \[ \frac{L}{10} = \log \left( \frac{I}{I_0} \right) \] \[ 10^{\frac{L}{10}} = \frac{I}{I_0} \] \[ I = I_0 \times 10^{\frac{L}{10}} \] 3. **Calculate the Sound Intensity:** \[ I = 1 \times 10^{-12} \, W/m^2 \times 10^{\frac{70}{10}} \] \[ I = 1 \times 10^{-12} \, W/m^2 \times 10^7 \] \[ I = 1 \times 10^{-5} \, W/m^2 \] 4. **Relation Between Intensity and Power:** \[ I = \frac{P}{A} \] Here, \( P \) is the power and \( A \) is the surface area of a sphere with radius \( r = d \): \[ A = 4 \pi d^2 \] Hence, \[
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