Question

Assertion :A $80dB$ sound has twice the intensity of a $40dB$ sound. Reason: Loudness of a sound of a certain intensity I is defined as
$L_{dB}=10{\log }_{10}{\frac{I}{I}}_o$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason are correct

Answer 1

The correct option is D Assertion is incorrect but Reason are correct

Since
$L_{db}=10{\log }_{10}\frac{I}{I_0}$
for 80 db,

$80=10{\log }_{10}\frac{I}{I_0}$

$\frac{I}{I_0}={10}^8$

$I_{80db}={10}^8\times I_0$
for 40 db,
$40=10{\log }_{10}\frac{I}{I_0}$

$\frac{I}{I_0}={10}^4$

$I_{40db}={10}^4\times I_0$

$\frac{I_{80db}}{I_{40db}}={10}^4$
Option "D" is correct.