Question

A two-fold increase in intensity of a wave implies an increase of (Given: ${\text{log}}_{10}2=0.3010$)

• A. $2\text{dB}$
• B. $10\text{dB}$
• C. $3.01\text{dB}$
• D. $0.5\text{dB}$

Answer 1

The correct option is C $3.01\text{dB}$

$L=10{\text{log}}_{10}\frac{I}{I_0}\text{dB}$
$L^{{}^{\prime }}=10{\text{log}}_{10}\frac{2I}{I_0}\text{dB}$
$\Rightarrow L^{{}^{\prime }}-L=10[{\text{log}}_{10}\frac{2I}{I_0}-{\text{log}}_{10}\frac{I}{I_0}]$
$\Rightarrow \Delta L=10{\text{log}}_{10}2=10\times 0.3010=3.01\text{dB}$