QuestionApril 24, 2025

Does doubling the sound intensity double the sound intensity level (decibel level)? Yes No Explain. square This answer has not been graded yet.

Does doubling the sound intensity double the sound intensity level (decibel level)? Yes No Explain. square This answer has not been graded yet.
Does doubling the sound intensity double the sound intensity level (decibel level)?
Yes
No
Explain.
square 
This answer has not been graded yet.

Solution
4.1(280 votes)

Answer

No Explanation 1. Understand the relationship between intensity and decibel level Sound intensity level in decibels is calculated using the formula: **L = 10 \log_{10} \left(\frac{I}{I_0}\right)**, where L is the sound level in decibels, I is the intensity, and I_0 is the reference intensity. 2. Analyze the effect of doubling intensity If intensity I is doubled to 2I, the new level L' becomes: **L' = 10 \log_{10} \left(\frac{2I}{I_0}\right) = 10 \log_{10} \left(2\right) + 10 \log_{10} \left(\frac{I}{I_0}\right)**. 3. Calculate the change in decibel level The change in decibel level \Delta L is: **\Delta L = L' - L = 10 \log_{10} (2) \approx 3 \text{ dB}**. Doubling intensity increases the level by approximately 3 dB, not double.

Explanation

1. Understand the relationship between intensity and decibel level<br /> Sound intensity level in decibels is calculated using the formula: **$L = 10 \log_{10} \left(\frac{I}{I_0}\right)$**, where $L$ is the sound level in decibels, $I$ is the intensity, and $I_0$ is the reference intensity.<br /><br />2. Analyze the effect of doubling intensity<br /> If intensity $I$ is doubled to $2I$, the new level $L'$ becomes: **$L' = 10 \log_{10} \left(\frac{2I}{I_0}\right) = 10 \log_{10} \left(2\right) + 10 \log_{10} \left(\frac{I}{I_0}\right)$**.<br /><br />3. Calculate the change in decibel level<br /> The change in decibel level $\Delta L$ is: **$\Delta L = L' - L = 10 \log_{10} (2) \approx 3 \text{ dB}$**. Doubling intensity increases the level by approximately 3 dB, not double.
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