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Q.

Sound waves are emitted uniformly in all direction from a point source. The dependence of sound level $β$ in decibels at distance ‘r’ can be expressed as ( a and b are constants)

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a

$β = - b \log r^{a}$

b

$β = a - b {(\log r)}^{2}$

c

$β = a - b \log r$

d

$β = a - (\frac{b}{r^{2}})$

answer is C.

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Detailed Solution

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Intensity at a distance r from isotropic point source of sound having power P is given by
$\begin{array}{l} I = \frac{P}{4 π r^{2}} \\ S L = 10 \log \frac{I}{I_{0}} = 10 [\log \frac{P}{4 π r^{2}} - \log I_{0}] \\ = 10 [\log p - \log 4 - \log I_{0}] - 20 \log r \\ = a - b \log r \end{array}$

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Sound waves are emitted uniformly in all direction from a point source. The dependence of sound level β in decibels at distance ‘r’ can be expressed as ( a and b are constants)