If the frequency of sound produced by a siren increases from $400\text{ Hz}$ to $1200\text{ Hz}$ while the…

If the frequency of sound produced by a siren increases from $400\text{ Hz}$ to $1200\text{ Hz}$ while the wave amplitude remains constant, the ratio of the intensity of the $1200\text{ Hz}$ to that of the $400\text{ Hz}$ wave will be
  1. 1 : 1
  2. 1 : 3
  3. 3 : 1
  4. 9 : 1

Solution

Intensity, $I = \frac{1}{2} \rho \omega^2 A^2 v$ or $I \propto \omega^2$ or $I \propto f^2$ $\therefore \frac{I_2}{I_1} = \left(\frac{f_2}{f_1}\right)^2 = \left(\frac{1200}{400}\right)^2 = 9$

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