Question

3. A fan at a rock concert is 30 m from the stage, and at this point the sound intensity is 110 dB. a. How much energy is transferred to her eardrums each second b. What is the sound intensity at a distance of 100 m from the stage.

Answer 1

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

$\beta=10\log\dfrac{I}{I_{0}}$

Put the value into the formula

$110=10\log\dfrac{I}{1.0\times10^{-12}}$

$\dfrac{110}{10}=\log\dfrac{I}{1.0\times10^{-12}}$

$11=\log\dfrac{I}{1.0\times10^{-12}}$

$I=e^{11\times1.0\times10^{-12}}$

$I=1.00\ W/m^2$

We need to calculate the power

Using formula of power

$P=I\times A$

Put the value into the formula

$P=1.0\times\pi\times(30)^2$

$P=2827.4\ W$

(a). We need to calculate the energy is transferred to her eardrums each second

Using formula of energy

$E=P\times t$

$E=2827.4\times1$

$E=2827.4\ J$

Hence, (a). The energy is transferred to her eardrums each second is 2827.4 J

(b). The sound intensity is 1.00 W/m²