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JEE Mains · Physics · STD 11 - 14. waves and sound
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 \(10\,mm\)
- B \(\frac{3}{100}\, mm\)
- C \(1\, mm\)
- D \(\frac{1}{10}\, mm\)
Answer & Solution
Correct Answer
(B) \(\frac{3}{100}\, mm\)
Step-by-step Solution
Detailed explanation
\(\Delta p = B k S_{0}\) \(=\rho v ^{2} \times \frac{\omega}{ v } \times S _{0}\) \(\Rightarrow S _{0}=\frac{\Delta p }{\rho v \omega}\) \(\approx \frac{10}{1 \times 300 \times 1000} m\) \(=\frac{1}{30} mm \approx \frac{3}{100} mm\)
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