Question

If the intensity of sound is increased by a factor of 30 , by how many decibels is the sound level increased ?

• A. 12 dB
• B. 14.77 dB
• C. 10 dB
• D. 13 dB

Answer 1

The correct option is B 14.77 dB

The intensity of sound in increased by factor $30$

Let $2$ be the intensity of previous sound

Intensity of recent sound $I=30I$

$\beta =10\log \frac{I}{I_o}$

${\beta }_1=10\log \frac{I}{I_o}$ where intensity of sound is $I$

${\beta }_1=10\log \frac{30I}{I_o}$ when intensity of sound is $I$

Increased in sound level $\Rightarrow {\beta }_2-{\beta }_1$

$=10\log \frac{30I}{I_o}-10\log \frac{I}{I_o}$

$=10\log 30$

$10\log \frac{30I}{I}$

$=14.77d\beta$.