Calculate the bulk modulus of air from the following data about a sound wave of wavelength 35 cm travelling in air. The pressure at a point varies between $(1.0 \times 10^{5} \pm 20) Pa$ and the particle of the air vibrate in simple harmonic motion of amplitude $5.6 \times 10^{- 6} m$ .

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$4 \times 10^{6}$

$4 \times 10^{2}$

$4 \times 10^{4}$

$4 \times 10^{8}$

answer is B.

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Detailed Solution

${ΔP}_{0} = 20 Pa$

$δ_{0} = 5.6 \times 10^{- 6} m$

$λ = 35 cm \Rightarrow 35 / 100 m$

$k = \frac{2 π}{λ} \Rightarrow \frac{2 π}{35} \times 100$

$k = \frac{40 π}{7}$

${ΔP}_{0} = {Bkδ}_{0}$

$B = \frac{{ΔP}_{0}}{{kδ}_{0}}$

$= \frac{7 \times 20}{40 π \times 5.6 \times 10^{- 6}} = \frac{1}{25} \times 10^{6} N / m^{2}$

$B = 4 \times 10^{4} N / m^{2}$

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