Question

Intensities of a sound as observed at distances 5m and 10m from it's source are in ratio?
2:1
3:1
✓2:1
Or 4:1?

Answer 1

Given:

Intensity of sound is observed at 5m and 10 m from the source.

To find:

Ratio of intensity?

Calculation:

Let intensity be I :

$\boxed{ \rm \: I \propto \: \dfrac{1}{ {r}^{2} } }$

Now, required ratio :

$\rm\therefore \: \dfrac{ I_{1}}{I_{2}} = \dfrac{ {(r_{2})}^{2} }{ {( r_{1})}^{2} }$

$\rm\implies \: \dfrac{ I_{1}}{I_{2}} = \dfrac{ {(10)}^{2} }{ {(5)}^{2} }$

$\rm\implies \: \dfrac{ I_{1}}{I_{2}} = \dfrac{100 }{25 }$

$\rm\implies \: \dfrac{ I_{1}}{I_{2}} = \dfrac{4}{1}$

$\rm\implies \: I_{1} : I_{2} = 4 : 1$

So , the required ratio is 4 : 1