wave_mechanics musical_sound Question 22
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
Options:
A) 1 : 4
B) 1 : 2
C) 1 : 104
D) 1 : 102
Show Answer
Answer:
Correct Answer: D
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}} $
Therefore $ 4={\log _{10}}\frac{I _{2}}{I _{1}} $
Therefore $ \frac{I _{2}}{I _{1}}=10^{4} $
Therefore $ \frac{a _{2}^{2}}{a _{1}^{2}}=10^{4} $
Therefore $ \frac{a _{2}}{a _{1}}=\frac{10^{2}}{1} $
Therefore $ \frac{a _{1}}{a _{2}}=\frac{1}{10^{2}} $
BETA
