Question
Download Solution PDFThe first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm. The length of the open organ pipe is ________ cm.
Answer (Detailed Solution Below) 26.66 - 27
Detailed Solution
Download Solution PDFCONCEPT:
When an organ pipe is opened from both ends, its frequency is written as;
f =
and when it is closed then its frequency is written as;
f' =
CALCULATION:
Given: Length, L' = 20 cm
Let us suppose P1 is the open pipe and its frequency is written as;
f1 =
and P2 is the closed organ pipe and its frequency is written as;
f2 =
It is given that the first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe, therefore we have,
f1 = f'2
⇒
⇒
Now, on putting the value of length we have;
L =
⇒ L =
⇒ L = 26.66 cm
Hence, the length of an open organ pipe, L = 26.66 cm.
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