Question

The intensity level due to two waves of the same frequency in a given medium are 1 bel and 5 bel. Then the ratio of amplitudes is

• A. 1 : 4
• B. 1 : 2
• C. 1 : 10⁴
• D. 1 : 10²

Answer 1

Answer: (D)

1 : 10²

Answer 2

By using $L = \log_{10}\frac{I}{I_{0}}$

$L_{2} - L_{1} = \log_{10}\frac{I_{2}}{I_{0}} - \log_{10}\frac{I_{1}}{I_{0}}$

$5 - 1 = \log_{10}\frac{I_{2}}{I_{1}}$⇒ $4 = \log_{10}\frac{I_{2}}{I_{1}}$⇒ $\frac{I_{2}}{I_{1}} = 10^{4}$

⇒ $\frac{a_{2}^{2}}{a_{1}^{2}} = 10^{4}$⇒ $\frac{a_{2}}{a_{1}} = \frac{10^{2}}{1}$⇒ $\frac{a_{1}}{a_{2}} = \frac{1}{10^{2}}$