Assertion Sound produced by an open organ pipe is richer than the sound produced by a closed organ pipe.…
Assertion Sound produced by an open organ pipe is richer than the sound produced by a closed organ pipe.
Reason Outside air can enter the pipe from both ends, in case of open organ pipe.
(a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(b) If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
(c) If Assertion is correct but Reason is incorrect.
(d) If Assertion is incorrect but Reason is correct.
Solution
Open organ pipes support all harmonics (both even and odd), so the sound is richer. For the same length $L$ the fundamental frequencies are
open pipe: $f_{open}=\dfrac{v}{2L}$, closed pipe: $f_{closed}=\dfrac{v}{4L}$,
so $f_{open}=2f_{closed}$.
Both sentences are true; the Reason (relation between fundamentals) does not by itself explain the first sentence (richer sound), hence the given choice.