Sound with intensity larger than 120dB appears painful to a person. A small speaker delivers 2.0 W of audio output. How close can the person get to the speaker without hurting his ears?
Physics · Wave Motion
JEE Mains Advanced

Question

Sound with intensity larger than 120dB appears painful to a person. A small speaker delivers 2.0 W of audio output. How close can the person get to the speaker without hurting his ears?

G1 Physics · Accepted Answer

Step 1: Sound level β = 10 log₁₀(I/I₀) dB. Step 2: For a point source I ∝ 1/r²; for a harmonic wave I ∝ A²ω². Step 3: Apply the specified intensity, distance or amplitude ratio. Final: 40.