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Q.

Assertion (A) : An open organ pipe of certain length have the same fundamental frequency as closed organ pipe of half the length.
Reason (R) : In the case of open organ pipe, at both the ends antinodes are formed, while in the closed organ pipe at one end antinode and at the other end node is formed.

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a

A is false but R is true

b

Both A & R are true but R is not the correct explanation of A

c

Both A & R are true and R is correct explanation of A.

d

A is true but R is false.

answer is B.

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Detailed Solution

$n_{o p e n} = \frac{V}{2 l_{o}}; n_{c l o s e d} = \frac{V}{4 l_{c}}$

$f o r n_{o p e n} = n_{c l o s e d}, l_{c} = \frac{l_{o}}{2}$

Antinode forms at open end while node forms at closed end.

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Assertion (A) : An open organ pipe of certain length have the same fundamental frequency as closed organ pipe of half the length.Reason (R) : In the case of open organ pipe, at both the ends antinodes are formed, while in the closed organ pipe at one end antinode and at the other end node is formed.