Answer:
Explanation:
In the decibel scale , intensity of sound changes logarithmically as follows
[tex]10log\frac{I}{I_0} =[/tex] Value in decibel scale , the value of I₀ = 10⁻¹² W /m².
Putting the values
[tex]10log\frac{I}{10^{-12}} = 71[/tex]
[tex]log\frac{I}{10^{-12}} = 7.1[/tex]
[tex]\frac{I}{10^{-12}} = 10^{7.1}[/tex]
[tex]I= 10^{-4.9}[/tex] W/m²
Similarly for 54 dB sound intensity can be given as follows
I = 10⁻¹² x [tex]10^{5.4}[/tex]
[tex]I= 10^{-6.6 }[/tex] W / m²
For intensity of sound the relation is as follows
I = 2π²υ²A²ρc where υ is frequency , A is amplitude , ρ is density of air and c is velocity of sound .
Putting the given values for 71 dB
[tex]I= 10^{-4.9}[/tex] = 2π² x 504²xA²x 1.21 x 346
A² = 60.03 x 10⁻¹⁶
A = 7.74 x 10⁻⁸ m
For 54 dB sound
[tex]10^{-6.6}[/tex] = 2π² x 504²xA²x 1.21 x 346
A² = 1.1978 x 10⁻¹⁶
A = 1.1 x 10⁻⁸ m
