Question

A rock band gives rise to an average sound level of $100\text{dB}$ at a distance $20\text{m}$ from the centre of the band. As an approximation, assume that the sound radiated by the band spreads out in the shape of a sphere centred at the band. What is the power of sound produced by the band?

• A. $80\text{W}$
• B. $50\text{W}$
• C. $20\text{W}$
• D. $10\text{W}$

Answer 1

The correct option is B $50\text{W}$

Given that,
$\beta =100\text{dB}$
From formula,
$\beta =10\log \left(\frac{I}{I_0}\right)$
$\Rightarrow 100=10\log \left(\frac{I}{{10}^{-12}}\right)$
[$I_0=$ threshold of hearing $={10}^{-12}{\text{W/m}}^2$]

$\Rightarrow I={10}^{-2}{\text{W/m}}^2$
Intensity $=\frac{\text{Power}}{\text{Area}}=\frac{P}{4\pi r^2}$
[since sound spreads out in the shape of a sphere]
$\Rightarrow P=I\times 4\pi r^2$
$={10}^{-2}\times 4\pi \times (20{)}^2$
$=50.26\text{W}\simeq 50\text{W}$