If the frequency of sound produced by a siren increases from 400 Hz to 1200 Hz while the wave amplitude remains constant, the ratio of the intensity of the 1200 Hz to that of the 400 Hz wave will be

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If the frequency of sound produced by a siren increases from 400 Hz to 1200 Hz while the wave amplitude remains constant, the ratio of the intensity of the 1200 Hz to that of the 400 Hz wave will be

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3 : 1

9 : 1

1 : 3

1 : 1

answer is D.

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Detailed Solution

Intensity, $I = \frac{1}{2} ρ ω^{2} A^{2} v or I \propto ω^{2} or I \propto f^{2}$

$∴ \frac{I_{2}}{I_{1}} = {(\frac{f_{2}}{f_{1}})}^{2} = {(\frac{1200}{400})}^{2} = 9$

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