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The maximum pressure variation that the human ear can tolrate is 30 N/m2. The maximum displacement for a sound wave in air having frequency of 103 kHz.

  • Option 1)

    \frac{2\pi}{3} \times 10^{-2}\; m

  • Option 2)

    \frac{2\times 10^{-4}}{\pi}\; m

  • Option 3)

    \frac{\pi}{3} \times 10^{-2}\; m

  • Option 4)

    \frac{10^{-4}}{3\pi}\; m

 

Answers (1)

best_answer

(\Delta P_{max}) = BAK \Rightarrow A =\frac{\Delta P}{BK}

v = \frac{\omega}{k}

k = \omega \sqrt{\frac{\rho}{B}} \Rightarrow A = \frac{\Delta P_{max}}{2\pi f \rho v } = \frac{10^{-4}}{3 \pi} m

 

 

Equation of sound wave -

\Delta P= \Delta P_{max}\cdot \sin\left [ \omega \left ( t-\frac{x}{V} \right ) \right ]
 

 

- wherein

\Delta P= variation in pressure at a point

\Delta P_{max}= maxmium variation in pressure

 

 

 


Option 1)

\frac{2\pi}{3} \times 10^{-2}\; m

This is incorrect.

Option 2)

\frac{2\times 10^{-4}}{\pi}\; m

This is incorrect.

Option 3)

\frac{\pi}{3} \times 10^{-2}\; m

This is incorrect.

Option 4)

\frac{10^{-4}}{3\pi}\; m

This is correct.

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Aadil

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