Assume that the displacement$(s)$ of air is proportional to the pressure difference $(\Delta p)$ created by a sound wave. Displacement$(s)$ further depends on the speed of sound $(v),$ density of air $(\rho)$ and the frequency $(f)$ If $\Delta p \approx 10\, Pa , v \approx 300\, m / s , p \approx 1\, kg / m ^{3}$ and $f \approx 1000 \,Hz$, then $s$ will be the order of
(take multiplicative constant to be $1$ )
JEE MAIN 2020, Diffcult
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$\Delta p = B k S_{0}$
$=\rho v ^{2} \times \frac{\omega}{ v } \times S _{0}$
$\Rightarrow S _{0}=\frac{\Delta p }{\rho v \omega}$
$\approx \frac{10}{1 \times 300 \times 1000} m$
$=\frac{1}{30} mm \approx \frac{3}{100} mm$
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