Question

For a sound source of intensity $IW/m^2$, corresponding sound level is $B_0$ decibel. If the intensity is increased to $4I$, new sound level becomes approximately :

• A. $2B_{0}dB$
• B. $(B_0+3)dB$
• C. $(B_0+6)dB$
• D. $4B_{0}dB$

Answer 1

The correct option is C $(B_0+6)dB$

Since, the sound level is $B_o$, for

the sound source of Intensity $IW{m}^{-2}$

$\Rightarrow B_o=10Log\frac{I}{I_o}...\left(i\right)$

where,

$I_o={10}^{-12}W{m}^{-2}$

when the sound increased is increased

to $4I,$ Let the new sound

level be 'B'

$\Rightarrow B=10log\frac{4I}{I_o}$

$\Rightarrow B=10[log\frac{I}{I_o}+log4]\because \left[\begin{array}{c}log{a}^b\\ =loga+\\ logb\end{array}\right]$

$\Rightarrow B=10log\frac{I}{I_o}+10log4$

$B=B_o+10\times 0.60$

$\Rightarrow B=(B_o+6)dB$