The sound level at a point 5.0 m away from a point source is 40 dB. What will be the level at a point 50 m away from the source ?

Answer

2

Explanation

We know that `beta=10log_(10)((I)/(I_(0)))`
`beta_(A)=10log_(10)(I_(A))/(I_(0))`
`beta_(B)=10log((I_(B))/(I_(0)))`
`(I_(A))/(I_(0))=10((beta_(A))/(10))`
`(beta_(A)-beta_(B))/(10)=2log10`
`(I_(A))/(I_(B))=(r_(B)^(2))/(r_(A)^(2))=((50)/(5))^(2)`
`((beta_(A)-beta_(B))/(10))=2`
`beta_(A)-beta_(B)=20`
`beta_(B)=40-20=20dB`