Two harmonic waves traveling in the same medium have frequency ratio 1 : 2 and intensity ratio 1 : 36. Their amplitude ratio is

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1:3

1:72

1:6

1:8

answer is A.

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Detailed Solution

$I n t e n s i t y I \infty a^{2} ω^{2} \frac{I_{1}}{I_{2}} = \frac{a_{1}^{2} ω_{1}^{2}}{a_{2}^{2} ω_{2}^{2}} or \frac{1}{36} = \frac{a_{1}^{2}}{a_{2}^{2}} \cdot \frac{1}{4} or \frac{a_{1}}{a_{2}} = \frac{1}{3}$

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