એક બિંદુવત્ત ઉદગમ ઉગમબિંદુ આગળ \(16 \times 10^{-8} \mathrm{Wm}^{-2}\) ની તીવ્રતાથી ધ્વનિ તરંગો ઉત્પન્ન કરે છે. ઉગમબિંદુથી અનુક્રમે \(2 m\) અને \(4 m\) અંતરે રહેલા બિંદુંઓ આગળ તીવ્રતાનો તફાવત (ફક્ત માનાંક) _______ \(\times 10^{-8} \mathrm{Wm}^{-2}\) છે.

A \(3\)
B \(2\)
C \(1\)
D \(5\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(3\)

Step-by-step Solution

Detailed explanation

Correct answer is : \(3\) We know for point source, \(I \propto \frac{1}{r^2}=\frac{K}{4 \pi r^2}\) \(r_1=2 m, r_2=4 m=2 r_1 \) \(I_0=16 \times 10^{-8} W / m ^2\) at \(2 m\), \(I_1=\frac{I_0}{(2)^2}=\frac{16 \times 10^{-8}}{4} \) \(I_1=4 \times 10^{-8} \)…

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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