Question

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

[Given reference intensity of sound as 10^-12W/m²]

Options

• 40 cm

• 20 cm

• 10 cm

• 30 cm

Answer 1

40 cm

Explanation:

Loudness (dB) = `10log_10(I_2/I_{ref})`

or 120 = `10log_10(I/(10^-12))` ⇒ I = 1

Also I = `P/(4pir^2) = 2/(4pir^2) ⇒ 1 = 1/(4pir^2) ⇒ r = sqrt(1/(2pi))`

⇒ r = 40 cm