બે મોટરકાર એકબીજા તરફ \(7.2\, km/hr\) ની ઝડપથી ગતિ કરે છે. તેઓ જ્યારે એકબીજાને જોઈને બંને \(676\,Hz\) આવૃત્તિવાળું હોર્ન વગાડે છે. બંને ડ્રાઈવરોને સંભળાતા સ્પંદની આવૃત્તિ ...... \(Hz\) છે. \([\) ધ્વનિની હવામાં વેગ \(340\, m/s\) છે.\(]\)

A \(8\)
B \(16\)
C \(32\)
D \(24\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(8\)

Step-by-step Solution

Detailed explanation

Frequency of sound heard by car\(-1,\) which comes by reflection from car\(-2\) \(f _{1}= f _{0}\left(\frac{340+2}{340-2}\right)\left(\frac{340+2}{340-2}\right)\) \(= f _{0}\left(\frac{342}{338}\right)^{2}\) Frequency of sound coming directly from car\(-2\)…

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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