First slide

Travelling wave

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

Moderate

A

1 : 4
B

1 : 2
C

1 : 10⁴
D

1 : 10²

Solution

By using $L = \log_{10} \frac{I}{I_{0}}$
$L_{2} - L_{1} = \log_{10} \frac{I_{2}}{I_{0}} - \log_{10} \frac{I_{1}}{I_{0}}$
$5 - 1 = \log_{10} \frac{I_{2}}{I_{1}} \Rightarrow 4 = \log_{10} \frac{I_{2}}{I_{1}} \Rightarrow \frac{I_{2}}{I_{1}} = 10^{4}$
$\Rightarrow \frac{a_{2}^{2}}{a_{1}^{2}} = 10^{4} \Rightarrow \frac{a_{2}}{a_{1}} = \frac{10^{2}}{1} \Rightarrow \frac{a_{1}}{a_{2}} = \frac{1}{10^{2}}$

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