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  • Assume that the displacement of air is proportional to the pressure difference <img alt="\left ( \Delta p \right )" src="http://entrancecorner.codecogs.com/gif.latex?%5Cl

Assume that the displacement (s) of air is proportional to the pressure difference \left ( \Delta p \right ) created by a sound wave. Displacement (s) further depends on the speed of sound \left ( \vartheta \right ), density of air \left ( \rho \right ) and the frequency \left ( f \right ). If \Delta p\sim 10Pa,\; \vartheta \sim 300 m/s,\; \rho \sim 1\; kg/m^{3} and f-1000\; Hz, then s will be of the order pf (take the multiplicative constant to be 1)
Option: 1 \frac{3}{100}mm
Option: 2 10\: mm
Option: 3 \frac{1}{10}\: mm
Option: 4 1\: mm

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\begin{array}{l} \because \Delta P_{0}=\mathbf{B} \frac{\omega}{\mathbf{v}} \times \mathbf{S}_{0} \\ \\ \Rightarrow \mathbf{S}=\frac{\Delta \mathbf{P} \times \mathbf{v}}{\mathbf{B} \omega}=\frac{\Delta \mathbf{P} \times \mathbf{v}}{\rho \mathbf{v}^{2} \times \mathbf{2} \pi v} \\ \\ \Rightarrow \mathbf{S} \propto \frac{\Delta \mathbf{P}}{\rho \mathbf{v f}} \\ \\ \Rightarrow \quad \mathbf{S}=\frac{\Delta P}{\rho \mathbf{P}} \\ \\ =\frac{10}{1 \times 300 \times 1000} \\ \\ =\frac{1}{30} \mathrm{~mm} \\ \\ \quad \approx \frac{3}{100} \mathrm{~mm} \end{array}

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Deependra Verma

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