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14. waves and sound — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
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 $1$ )

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

Answer

Correct option: B.
$\frac{3}{100}\, mm$
b
$\Delta p = B k S_{0}$

$=\rho v ^{2} \times \frac{\omega}{ v } \times S _{0}$

$\Rightarrow S _{0}=\frac{\Delta p }{\rho v \omega}$

$\approx \frac{10}{1 \times 300 \times 1000} m$

$=\frac{1}{30} mm \approx \frac{3}{100} mm$

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