ચામાચીડિયું \(10\,ms^{-1}\) ના વેગથી દીવાલ તરફ \(8000\,Hz\) આવૃતિવાળા ધ્વનિના તરંગો મોકલે છે. જે અથડાયને પાછો આવે ત્યારે ચામાચીડિયાને \(f\) આવૃતિવાળા ધ્વનિના તરંગો સંભળાય છે. તો \(f\) નું મૂલ્ય \(Hz\)માં કેટલું હશે? (ધ્વનિની ઝડપ\(= 320\,ms^{-1}\) )

A \(8516\)
B \(8258\)
C \(8424\)
D \(8000\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(8516\)

Step-by-step Solution

Detailed explanation

Reflected frequency of sound reaching bat \( = \left[ {\frac{{V - \left( {{V_0}} \right)}}{{V - {V_s}}}} \right]f = \left[ {\frac{{V + {V_0}}}{{V - {V_s}}}} \right]f = \frac{{V + 10}}{{V - 10}}f\) \( = \left( {\frac{{320 + 10}}{{320 - 10}}} \right) \times 8000 = 8516Hz\)

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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