Question

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 $\Delta∼ p-10 \,Pa , \quad v \sim 300 m / s , p∼ 1 \,kg / m ^{3}$ and $f ∼1000\, Hz$, then $s$ will be the order of (take multiplicative constant to be 1 )

• A. $10 \,mm$
• B. $\frac{3}{100} \,mm$
• C. $1\, mm$
• D. $\frac{1}{10} \,mm$

Answer 1

Answer: (B)

$\Delta p=B k S_{0}$
$=\rho v^{2} \times \frac{\omega}{v} \times S_{0}$
$\Rightarrow S_{0}=\frac{\Delta p}{\rho v \omega}$
$\approx \frac{10}{1 \times 300 \times 1000} m$
$=\frac{1}{30} mm \approx \frac{3}{100}\, mm$