Question

A harvest mouse can detect sounds below the threshold of human hearing, as quiet as −10 dB. Suppose you are sitting in a field on a very quiet day while a harvest mouse sits nearby. A very gentle breeze causes a leaf 1.5 m from your head to rustle, generating a faint sound right at the limit of your ability to hear it. The sound of the rustling leaf is also right at the threshold of hearing of the harvest mouse. How far is the harvest mouse from the leaf?

Answer 1

Answer:

The distance from harvest mouse to the leaf is 4.74 m.

Explanation:

Given that,

Intensity = -10 dB

Distance = 1.5 m

We need to calculate the power of intensity

Using formula of power of intensity

$P=I_{0}A$

$P=I_{0}\times4\pi r^2$

Put the value into the formula

$P=1.0\times10^{-12}\times4\pi\times(1.5)^2$

$P=28.27\times10^{-12}\ W/m^2$

We need to calculate the minimum intensity level

Using formula of minimum intensity

$I=10\log_{10}(\dfrac{I}{I_{0}})$

$-10=10\log_{10}(\dfrac{I}{I_{0}})$

$\log_{10}\dfrac{I}{I_{0}}=-1$

$I=10^{-1}\times(1.0\times10^{-12})$

$I=1\times10^{-13}\ W/m$

We need to calculate the area

Using formula of intensity

$I=\dfrac{P}{A}$

$A=\dfrac{P}{I}$

Put the value into the formula

$A=\dfrac{28.27\times10^{-12}}{1\times10^{-13}}$

$A=282.7\ m^2$

We need to calculate the distance

Using formula of area

$A=4\pi r^2$

Put the value into the formula

$282.7=4\pi\times r^2$

$r^2=\dfrac{282.7}{4\pi}$

$r=\sqrt{\dfrac{282.7}{4\pi}}$

$r=4.74\ m$

Hence, The distance from harvest mouse to the leaf is 4.74 m.