A source of sound emits 200 π W power which is uniformly distributed over a sphere of 10 m radius. What is the loudness of sound on the surface of a sphere?

Question

A source of sound emits 200 π W power which is uniformly distributed over a sphere of 10 m radius. What is the loudness of sound on the surface of a sphere? (A) 200 dB (B) 200 π dB (C) 120 dB (D) 120 π dB

Tardigrade Admin · Accepted Answer

Intensity of sound, I=(P/A) =(200π /2π × (10)2) =1 W/m2 ∴ Loudness, L=10 text log 10(I/I0) =10 text log 10(1/10-12) =10 text log 101012 =120 dB.

Q. A source of sound emits 200 $π$ W power which is uniformly distributed over a sphere of 10 m radius. What is the loudness of sound on the surface of a sphere?

200 dB

200 $π$ dB

120 dB

120 $π$ dB

Intensity of sound, $I = \frac{P}{A}$ $= \frac{200 π}{2 π \times ( 10 ) ^{2}}$ $= 1 W / m^{2}$ $∴$ Loudness, $L = 10 lo g_{10} \frac{I}{I _{0}}$ $= 10 lo g_{10} \frac{1}{10 ^{- 12}}$ $= 10 lo g_{10} 10^{12}$ $= 120 d B .$

Q. A source of sound emits 200 π W power which is uniformly distributed over a sphere of 10 m radius. What is the loudness of sound on the surface of a sphere?

200 dB

200 π dB

120 dB

120 π dB

Intensity of sound, I=AP​ =2π×(10)2200π​ =1W/m2 ∴ Loudness, L=10log10​I0​I​ =10log10​10−121​ =10log10​1012 =120dB.

Q. A source of sound emits 200 $π$ W power which is uniformly distributed over a sphere of 10 m radius. What is the loudness of sound on the surface of a sphere?

200 $π$ dB

120 $π$ dB

Intensity of sound, $I = \frac{P}{A}$ $= \frac{200 π}{2 π \times ( 10 ) ^{2}}$ $= 1 W / m^{2}$ $∴$ Loudness, $L = 10 lo g_{10} \frac{I}{I _{0}}$ $= 10 lo g_{10} \frac{1}{10 ^{- 12}}$ $= 10 lo g_{10} 10^{12}$ $= 120 d B .$