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When a helicopter is hovering 1450 m directly overhead, anovserver on the ground measures a sound intensity I. Assume thatsound is radiated uniformly

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asked 2021-04-14
When a helicopter is hovering 1450 m directly overhead, anovserver on the ground measures a sound intensity I. Assume thatsound is radiated uniformly from the helicopter and that groundreflections are negligible. How far must the helicopter fly in astraight line parallel to the ground before the observer measures asound intensity of 0.25I?

Expert Answers (1)

2021-04-16
As we know that the intensity of sound waves is related to distance
\(\displaystyle{I}\alpha{\frac{{{1}}}{{{r}^{{{2}}}}}}\)
where I is the intensity of light
r is the distance between the source and the observer
so \(\displaystyle{\frac{{{I}_{{{1}}}}}{{{I}_{{{2}}}}}}={\frac{{{{r}_{{{2}}}^{{{2}}}}}}{{{{r}_{{{1}}}^{{{2}}}}}}}\)
we have \(\displaystyle{I}_{{{1}}}={I}\)
\(\displaystyle{I}_{{{2}}}={0.25}{I}\)
\(\displaystyle{r}_{{{1}}}={1450}{m}\)
substituting these values we get
\(\displaystyle{r}_{{{2}}}={2900}{m}\)
hence the helicopter must fly 2900m above the ground
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