Question

The intensity level due to two waves of the same frequency in a given medium are 1 dB and 4 dB. The ratio of their amplitude is

• A. $1:{10}^4$
• B. $1:4$
• C. $1:2$
• D. $1:{10}^{0.15}$

Answer 1

Answer: (D)

$1:{10}^{0.15}$

Loudness of the sound $L=10lo{g}_{10}\frac{I}{I_o}$

$L_2-L_1=10lo{g}_{10}\frac{I_2}{I_1}$

As intensity of the wave is directly proportional to the square of the

amplitude, i.e $I\propto A^2$

$⟹$ $L_2-L_1=20lo{g}_{10}\frac{A_2}{A_1}$

$4-1=20{\log }_{10}\frac{A_2}{A_1}$

Thus $\frac{A_2}{A_1}={10}^{0.15}$