Sound Loudness: Increase of 13.98 dB

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The discussion focuses on calculating the increase in loudness in decibels when sound intensity increases by a factor of 25. Using the formula dB = 10 log(Ib/Ia), the calculation shows that the increase is 13.98 dB. This result confirms the relationship between intensity and perceived loudness in sound. The solution is deemed correct, demonstrating a clear understanding of the logarithmic nature of sound intensity. Overall, the thread effectively illustrates the mathematical approach to sound loudness changes.
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Homework Statement



How many decibels does the loudness of a sound increase if its intensity increases 25 times?

Homework Equations



dB = 10 log\frac{I_{b}}{I_{a}}

The Attempt at a Solution



\frac{I_{b}}{I_{a}} = \frac{25}{1}

dB = 10 log\frac{25}{1}
dB = 13.98
 
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Correct.
 

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