devarshi-dt-logo

Question:

A small speaker delivers 2W of audio output. At what distance from the speaker will one detect 120dB intensity sound?

10cm

30cm

20cm

40cm

Solution:

Loudness of sound is given by dB = 10log(I/I₀) (I is intensity of sound, I₀ is reference intensity of sound)
∴ 120 = 10log(I/I₀) ⇒ I = 1 W/m²
Also I = P/4πr² = 2/4πr²
∴ r = √(2/4π) = √(1/2π) m = 0.399 m ≈ 40cm