Question

Sound with intensity larger than 120 dB 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?

• A. 40 cm
• B. 80 cm
• C. 120 cm
• D. 10 cm

Answer 1

The correct option is A

40 cm

Let's say the person can get to a closest distance of x.Then intensity at the distance I.

$I=\frac{power}{surfacearea}=\frac{2}{4\pi x^2}$

Loudness, $\beta =10log\left(\frac{I}{I_0}\right)=10log(\frac{2}{4\pi x^2}\times {10}^{12})$

$|(I_0=1.0\times {10}^{-12}\omega m^{-2})|$

${\beta }_{max}=120$

$120=10lo{g}_{10}(\frac{2}{4\pi x^2}\times {10}^{-12})$

$x=0.4m$