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marysya [2.9K]
3 years ago
9

The sound intensity from a jack hammer breaking concrete is 2.0W/m2 at a distance of 2.0 m from the point of impact. This is suf

ficiently loud to cause permanent hearing damage if the operator doesn't wear ear protection. What are (a) the sound intensity and (b) the sound intensity level for a person watching from 50 m away?
Physics
1 answer:
kupik [55]3 years ago
8 0

Answer:

(a) I_{1}=3.2*10^{-3}W/m^{2}

(b) \beta =95dB

Explanation:

Given data

Distance r₁=50 m

Distance r₂=2 m

Intensity I₂=2.0 W/m²

To find

(a) The Sound Intensity I₁

(b) The Sound Intensity level β

Solution

For (a) the Sound Intensity I₁

\frac{I_{1} }{I_{2}}=\frac{(r_{2})^{2}  }{(r_{1})^{2} }\\I_{1} =I_{2}(\frac{(r_{2})^{2}  }{(r_{1})^{2} })\\I_{1}=(2.0W/m^{2} )(\frac{(2m)^{2}  }{(50m)^{2} })\\I_{1}=3.2*10^{-3}W/m^{2}

For (b) the Sound Intensity level β

The Sound Intensity level β is calculated as follow

\beta =(10dB)log_{10}(\frac{I}{I_{o} } )\\\beta  =(10dB)log_{10}(\frac{3.2*10^{-3}W/m^{2}  }{1.0*10^{-12} W/m^{2} } )\\\beta =95dB

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