The sound from a trumpet is emitted uniformly in all directions at $20 ° C$ . At point ‘P’ in space the sound intensity level is 30 dB. The density of air in the medium is $1.5 k g / m^{3}$ , the velocity of sound at $20 ° C$ is 300 m/sec. Find the displacement amplitude (in $A °$ ) at point ‘P’. The frequency of sound wave in the medium is 600 Hz. $(T a k e π^{2} = 10)$

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Detailed Solution

$β = 10 \log \frac{I}{I_{0}}$

$3 = \log \frac{I}{10^{- 12}}$

$\Rightarrow I = 10^{- 9} W / m^{2}$

Now, $I = \frac{{(Δ P_{0})}^{2} V}{2 B} = \frac{{(B A K)}^{2} V}{2 B} = \frac{B ω^{2} A^{2}}{2 V} = \frac{B A^{2} 4 π^{2} f^{2}}{2 V}$

$A = \sqrt{\frac{I V}{B 2 π^{2} f^{2}}} = \sqrt{\frac{I}{ρ v 2 π^{2} f^{2}}} = 5.55$ $\overset{0}{A}$

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