Answer:
(a). The energy is transferred to her eardrums each second is 2827.4 J
(b). The sound intensity is 1.00 W/m²
Explanation:
Given that,
Distance = 30 m
Intensity = 110 dB
(b). We need to calculate the intensity
Using formula of intensity
[tex]\beta=10\log\dfrac{I}{I_{0}}[/tex]
Put the value into the formula
[tex]110=10\log\dfrac{I}{1.0\times10^{-12}}[/tex]
[tex]\dfrac{110}{10}=\log\dfrac{I}{1.0\times10^{-12}}[/tex]
[tex]11=\log\dfrac{I}{1.0\times10^{-12}}[/tex]
[tex]I=e^{11\times1.0\times10^{-12}}[/tex]
[tex]I=1.00\ W/m^2[/tex]
We need to calculate the power
Using formula of power
[tex]P=I\times A[/tex]
Put the value into the formula
[tex]P=1.0\times\pi\times(30)^2[/tex]
[tex]P=2827.4\ W[/tex]
(a). We need to calculate the energy is transferred to her eardrums each second
Using formula of energy
[tex]E=P\times t[/tex]
[tex]E=2827.4\times1[/tex]
[tex]E=2827.4\ J[/tex]
Hence, (a). The energy is transferred to her eardrums each second is 2827.4 J
(b). The sound intensity is 1.00 W/m²
