સીધા પાટા પર \(20\) \(ms^{-1}\) ઝડપથી એક ટ્રેન ગતિ કરે છે.તે \(1000\) \(Hz\) આવૃત્તિ ધરાવતી વ્હિસલ (સિસોટી) વગાડે છે.પાટા પાસે ઊભેલા એક વ્યકિતને ટ્રેન પસાર થાય ત્યારે સંભળાતી આવૃત્તિમાં થતો પ્રત્યાશીત ફેરફાર _________ \(\%\) .( ધ્વનિનો વેગ = \(320\) \(ms^{-1}\) ) ની નજીક થશે.

A \(12\)
B \(18\)
C \(24\)
D \(6\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(12\)

Step-by-step Solution

Detailed explanation

\(f_{1}=f\left[\frac{v}{v-v_{s}}\right]=f \times \frac{320}{300} \mathrm{Hz}\) \(f_{2}=f\left[\frac{v}{v+v_{s}}\right]=f \times \frac{320}{340} \mathrm{Hz}\) \(\left(\frac{f_{2}}{f_{1}}-1\right) \times 100=\left(\frac{300}{340}-1\right) \times 100 \simeq 12 \%\)

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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