Answer:
[tex]\dfrac{I_1}{I_2}=\dfrac{4}{9}[/tex]
Explanation:
c = Speed of wave
[tex]\rho[/tex] = Density of medium
A = Area
[tex]\nu[/tex] = Frequency
[tex]\nu_1=\dfrac{2}{3}\nu_2[/tex]
Intensity of sound is given by
[tex]I=\dfrac{1}{2}\rho c(A\omega)^2\\\Rightarrow I=\dfrac{1}{2}\rho c(A2\pi \nu)^2[/tex]
So,
[tex]I\propto \nu^2[/tex]
We get
[tex]\dfrac{I_1}{I_2}=\dfrac{\nu_1^2}{\nu_2^2}\\\Rightarrow \dfrac{I_1}{I_2}=\dfrac{\dfrac{2}{3}^2\nu_2^2}{\nu_2^2}\\\Rightarrow \dfrac{I_1}{I_2}=\dfrac{4}{9}[/tex]
The ratio is [tex]\dfrac{I_1}{I_2}=\dfrac{4}{9}[/tex]
