You are trying to overhear a juicy conversation, but from your distance of 24.0m , it sounds like only an average whisper of 40.0dB . So you decide to move closer to give the conversation a sound level of 80.0dB instead. How close should you come?

The distance is

Explanation:

From the question we are told that

       The  distance from the conversation is

       The  intensity of  the sound at your position is  

        The  intensity at the sound at the new position is  

Generally the intensity in  decibel is  is mathematically represented as

The intensity is  also mathematically represented as

So

=>  

From the logarithm definition

=>    

=>      

Here P is the power of the sound wave

 and  A is the cross-sectional area of the sound wave  which is generally in spherical form

Now the power of the sound wave at the first position is mathematically represented as

Now the power of the sound wave at the second  position is mathematically represented as

Generally  power of the wave is constant at both positions  so  

       substituting value

the part of the wave he is travelling on is the crest

no simpler subs form complex ones. synthesise = make