Question

For a sound source of intensity $1W/m^2$, corresponding sound level is $B_0$ decibel. If the intensity is increased to $4I$, new sound level becomes:

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

Answer 1

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

As we know, sound level is given by,

$\beta =10lo{g}_{10}\left(\frac{I}{I_0}\right)$

Sound level when the intensity of the source is $I$,

$B_0=10lo{g}_{10}\left(\frac{I}{I_0}\right)$

Let the sound level becomes $B^{\prime }$ when intensity increased to $4I$,

$B^{\prime }=10lo{g}_{10}\left(\frac{4I}{I_0}\right)$

Change in sound level,

$B^{\prime }-B_0=10[lo{g}_{10}\left(\frac{4I}{I_0}\right)-lo{g}_{10}\left(\frac{I}{I_0}\right)]$

$B^{\prime }-B_0=10\left[lo{g}_{10}(\frac{4I}{I_0}\times \frac{I_0}{I})\right]$

$B^{\prime }-B_0=10lo{g}_{10}\left(2^2\right)$

$=20\times 0.3010\approx 6$

$B^{\prime }=(B_0+6)dB$

Final answer : (c)