Question

If the intensity of sound is increased by a factor of $20$, by how many decibels is the sound level increased?

• A. $30dB$
• B. $14.77dB$
• C. $10dB$
• D. $13dB$

Answer 1

Answer: (A)

$30dB$

Let I and I’ be the old and new intensity of sound.

Then, according to the question

$I^{\prime }=20I$

$\frac{I^{\prime }}{I}=20$

We know that,

$\beta =10{\log }_e\left(\frac{I}{I_0}\right)$

Then change in sound level can be given as

$\Delta \beta ={\beta }_2-{\beta }_1$

$\Delta \beta =10{\log }_e\left(\frac{I^{\prime }}{I_0}\right)-10{\log }_e\left(\frac{I}{I_0}\right)$

$\Delta \beta =10{\log }_e\left(\frac{I^{\prime }}{I}\right)$

$\Delta \beta =10{\log }_e\left(20\right)$

$\Delta \beta =10\times 3$

$\Delta \beta =30dB$

Hence, the sound level increased $30dB$