AP EAMCET · PHYSICS · Waves and Sound

A closed organ pipe and an open organ pipe of same length produce $2 beats \sec^{- 1}$ when they are set into vibrations together in fundamental mode. The length of open pipe is now halved and that of closed pipe is doubled. The number of beats produced will be

A $7$
B $4$
C $8$
D $2$

Verified Solution

Answer & Solution

Correct Answer

(A) $7$

Step-by-step Solution

Detailed explanation

Fundamental frequency of closed organ pipe fc=v4l Fundamental frequency of open organ pipe fo=v2l Initial beats frequency fo-fc=2 ⇒v2l-v4l=2 ⇒v4l=2 ⇒vl=8 After changing of length Fundamental frequency of closed organ pipe fc'=v42l=v8l Fundamental frequency of…

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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A closed organ pipe and an open organ pipe of same length produce 2 beats sec-1 when they are set into vibrations together in fundamental mode. The length of open pipe is now halved and that of closed pipe is doubled. The number of beats produced will be

Step-by-step Solution

A closed organ pipe and an open organ pipe of same length produce $2 beats \sec^{- 1}$ when they are set into vibrations together in fundamental mode. The length of open pipe is now halved and that of closed pipe is doubled. The number of beats produced will be