A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 d B intensity sound? [Given reference intensity of sound as 10 - 12 W / m 2 ]

Step-by-step solution

Let the intensity of sound hear by observer is I 120 = 10 log 10 ⁡ I 10 - 12 12 = log ⁡ I - log 10 ⁡ 10 - 12 = log ⁡ I + 12 log ⁡ I = 0 ⇒ I = 1   w a t t m 2 I = P 4 π r 2 ⇒ 1 = 2 4 π r 2 ⇒ r = 1 2 π = 0.4   m = 40   c m