Question

The intensity level of the sound wave is said to be 4 decibels. If the intensity of the wave is doubled, then the intensity level of sound as expressed in decibel would be :

• A. $8$
• B. $16$
• C. $7$
• D. $14$

Answer 1

The correct option is C $7$

Intensity in dB unit is defined as

$I_{dB}=10{\log }_{10}\left(I/I_0\right)$.

If we double the intensity, the new intensity in dB will be

$I_{dB}^{\prime }=10{\log }_{10}\left(2I/I_0\right)=10{\log }_{10}\left(I/I_0\right)+10{\log }_{10}\left(2\right)=I_{dB}+10{\log }_{10}\left(2\right)=4+3=7$ dB.