A) 9 : 4
B) 2 : 3
C) 3 : 2
D) 4 : 9
Correct Answer: A
Solution :
Key Idea: The average power per unit area that is incident perpendicular to the direction of propagation is called the intensity. |
Intensity of sound |
\[I=\frac{P}{4\pi {{r}^{2}}}\] |
or \[I\,\propto \,\frac{1}{{{r}^{2}}}\] |
or \[\frac{{{I}_{1}}}{{{I}_{2}}}={{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{2}}\] |
Here, \[{{r}_{1}}=2\,m,\,{{r}_{2}}=3\,m\] |
Substituting the values, we have |
\[\frac{{{I}_{1}}}{{{I}_{2}}}={{\left( \frac{3}{2} \right)}^{2}}=\frac{9}{4}\] |
Note: As amplitude \[A\propto \sqrt{l},\] a spherical harmonic wave emanating from a point source can therefore, be written as: |
\[y(r,\,t)=\frac{A}{r}\sin (kr-\omega t)\] |
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