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Intensity of

Question

Sound waves are emitted uniformly in all directions from a point source. The dependence of sound level $β$ in decibels on the distance r can be expressed as (a and b are positive constants)

Moderate

A

$β = - b \log r^{2}$
B

$β = a - b {(\log r)}^{2}$
C

$β = a - b \log r$
D

$β = a - \frac{b}{r^{2}}$

Solution

$β = 10 \log \frac{I}{I_{0}}$
If P is power of sound source then
$β = 10 \log \frac{(\frac{P}{4 {πr}^{2}})}{I_{0}} where I_{0} = 10^{- 12} w / m^{2}$
= $10 \log \frac{P}{4 {πr}^{2} . I_{0}} = 10 [\log P - \log (4 {πI}_{0} . r^{2})]$
= 10[log P - log $4 {πI}_{0} - 2 \log r] = a - b \log r$
where a = 10 log P - 10 log $4 {πI}_{0} = constant and b = 20 = constant$

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