Question

Two sound waves of frequencies of 400 Hz and 300 Hz have an amplitude in the ratio 1 : 2. Then, the intensities of these waves will be in the ratio

• A. 4 : 3
• B. 1 : 4
• C. 16 : 9
• D. 4 : 9

Answer 1

The correct option is D 4 : 9

Let frequency of the sound wave be $\nu$ and displacement amplitude be $s_o$.

Given : $\nu =400Hz{\nu }^{\prime }=300Hz$ and $s_o:s_o^{\prime }=1:2$

Intensity of sound wave $I=2{\pi }^2{\nu }^2{s}_o^2\rho v$

where $\rho$ and $v$ are the density of medium and velocity of sound in that medium respectively.

$⟹I\propto {\nu }^2{s}_o^2$

Thus $\frac{I}{I^{\prime }}=\frac{{\nu }^2{s}_o^2}{\left({\nu }^{\prime }{)}^2\right(s_o^{\prime }{)}^2}=\frac{(400{)}^2}{(300{)}^2}\times \frac{1}{4}$

$⟹I:I^{\prime }=4:9$