## You are trying to overhear a juicy conversation, but from your distance of 20.0 m, it sounds like only an average whisper of 20.0 dB. So you

Question

You are trying to overhear a juicy conversation, but from your distance of 20.0 m, it sounds like only an average whisper of 20.0 dB. So you decide to move closer to give the conversation a sound level of 70.0 dB instead. How close should you come?

in progress 0
1 year 2021-08-22T05:38:54+00:00 1 Answers 33 views 0

1. Given that,

Distance = 20.0 m

Average whisper = 20.0 dB

Sound level = 70.0 dB

We know that,

The minimum intensity is

$$I_{o}=10^{-12}\ W/m^2$$

We need to calculate the sound intensity in the distance of 20 m

Using formula of sound intensity

$$dB=10\log(\dfrac{I_{a}}{I_{o}})$$

Put the value into the formula

$$20=10\log(\dfrac{I_{a}}{10^{-12}})$$

$$10^{2}=\dfrac{I_{a}}{10^{-12}}$$

$$I_{a}=10^{-10}\ W/m^2$$

If the conversation a sound level of 70.0 dB instead

We need to calculate the sound intensity

Using formula of sound intensity

$$dB=10\log(\dfrac{I_{b}}{I_{o}})$$

Put the value into the formula

$$70=10\log(\dfrac{I_{a}}{10^{-12}})$$

$$10^{7}=\dfrac{I_{b}}{10^{-12}}$$

$$I_{b}=10^{-5}\ W/m^2$$

We know that,

The intensity is inversely proportional with the square of the distance.

We need to calculate the distance

Using formula of intensity

$$\dfrac{I_{a}}{I_{b}}=\dfrac{R_{b}^2}{R_{a}^2}$$

Put the value into the formula

$$\dfrac{10^{-10}}{10^{-5}}=\dfrac{R_{b}^2}{20^2}$$

$$R_{b}^2=20^2\times\dfrac{10^{-10}}{10^{-5}}$$

$$R_{b}=\sqrt{20^2\times\dfrac{10^{-10}}{10^{-5}}}$$

$$R_{b}=0.063\ m$$

Hence, The distance from the conversation should be 0.063 m.