Discover new knowledge and insights with IDNLearn.com's extensive Q&A database. Discover comprehensive answers from knowledgeable members of our community, covering a wide range of topics to meet all your informational needs.
Sagot :
To solve for the sound intensity [tex]\( r \)[/tex] given that the sound level [tex]\( \beta \)[/tex] is 130 dB, we can use the formula [tex]\(\beta = 10 \log \left(\frac{r}{I_0}\right)\)[/tex], where [tex]\( I_0 \)[/tex] is the smallest sound intensity that can be heard by the human ear, approximately [tex]\( 10^{-12} \)[/tex] watts/meter[tex]\(^2\)[/tex].
Given:
[tex]\[ \beta = 130 \, \text{dB} \\ I_0 = 10^{-12} \, \text{watts/meter}^2 \][/tex]
Step-by-step solution:
1. Start with the formula:
[tex]\[ 130 = 10 \log \left(\frac{r}{10^{-12}}\right) \][/tex]
2. Divide both sides by 10 to isolate the logarithm:
[tex]\[ 13 = \log \left(\frac{r}{10^{-12}}\right) \][/tex]
3. Rewrite the logarithm equation in its exponential form:
[tex]\[ 10^{13} = \frac{r}{10^{-12}} \][/tex]
4. Solve for [tex]\( r \)[/tex]:
[tex]\[ r = 10^{13} \times 10^{-12} \][/tex]
5. Simplify the exponent:
[tex]\[ r = 10^{13-12} = 10^1 = 10 \][/tex]
Therefore, the sound intensity of a noise that is 130 dB is [tex]\( \boxed{10} \)[/tex] watts/meter[tex]\(^2\)[/tex].
Given:
[tex]\[ \beta = 130 \, \text{dB} \\ I_0 = 10^{-12} \, \text{watts/meter}^2 \][/tex]
Step-by-step solution:
1. Start with the formula:
[tex]\[ 130 = 10 \log \left(\frac{r}{10^{-12}}\right) \][/tex]
2. Divide both sides by 10 to isolate the logarithm:
[tex]\[ 13 = \log \left(\frac{r}{10^{-12}}\right) \][/tex]
3. Rewrite the logarithm equation in its exponential form:
[tex]\[ 10^{13} = \frac{r}{10^{-12}} \][/tex]
4. Solve for [tex]\( r \)[/tex]:
[tex]\[ r = 10^{13} \times 10^{-12} \][/tex]
5. Simplify the exponent:
[tex]\[ r = 10^{13-12} = 10^1 = 10 \][/tex]
Therefore, the sound intensity of a noise that is 130 dB is [tex]\( \boxed{10} \)[/tex] watts/meter[tex]\(^2\)[/tex].
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.