Question

Sound waves are emitted uniformly in ali directions from a point source. The dependence of sound level β in decibels on the distance r can be expressed as (a and b are positive constants)

• A. β =-b logr^a
• B. β=a-b(log r)²
• C. β= a - b log r
• D. β= a – b/r²

Answer 1

Answer: (C)

β= a - b log r

Answer 2

B = 10 log $\frac{I}{I_{0}}$

If P is power of sound source then

β = 10 log $\frac{\left( P/4\pi r^{2} \right)}{I_{0}}$where I_o = 10^-12w/m²

= 10 log $\frac{P}{4\pi r^{2}.I_{0}}$

= 10[logP-log(4πI₀.r²)]

= 10[logP-log4πI₀-2logr] = a- b log r where a = 10 log P - 10 log ρI₀

= constant b = 20 ⇒ constant