હવાના કણોનું સ્થાનાંતર \((s)\) એ ધ્વનિના તરંગ દ્વારા ઉત્પન્ન થતાં દબાણના તફાવત \((\Delta p)\) ના સમપ્રમાણમાં છે. સ્થાનાંતર \((s)\) એ ધ્વનિની ઝડપ \((v),\) હવાની ઘનતા \((\rho)\) અને આવૃતિ \((f)\) પર પણ આધાર રાખે છે. જો \(\Delta p \approx 10\, Pa , v \approx 300\, m / s , p \approx 1\, kg / m ^{3}\) અને \(f \approx 1000 \,Hz\) હોય તો \(s\) નું મૂલ્ય કયા ક્રમનું હશે? (ગુણકારનો અચળાંક \(1\) લો)

A \(10\,mm\)
B \(\frac{3}{100}\, mm\)
C \(1\, mm\)
D \(\frac{1}{10}\, mm\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{3}{100}\, mm\)

Step-by-step Solution

Detailed explanation

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

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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