The 4^ th overtone of a closed organ pipe is same as that of 3^ rd overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is:

Correct answer: A. 9: 8 4^ th overtone for closed organ pipe arrow 9^ th harmonic 3^ rd overtone for open organ pipe arrow 4^ th harmonic aligned & 9((V)/(4 I_c))=4((V)/(2 I_o)) & (I_c)/(I_o)=(9)/(8) aligned

NEET 2023

Exam: NEET
Year: 2023
Subject: Physics
Chapter: Waves and Sound

NEET 2023 · Physics · Waves and Sound

The 4^ th overtone of a closed organ pipe is same as that of 3^ rd...

The

4^{\text{th }}

overtone of a closed organ pipe is same as that of

3^{\text{rd }}

overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is:

Options

A $9: 8$
B $7: 9$
C $8: 9$
D $9: 7$

Correct answer

A. $9: 8$

Step-by-step solution

4^{\text{th }}overtone

for closed organ pipe \rightarrow 9^

{\text{th }} harmonic

{\text{rd }}

overtone for

open organ pipe \rightarrow 4^{\text{th }}

harmonic

\begin{aligned} & 9\left(\frac{V}{4 I_c}\right)=4\left(\frac{V}{2 I_o}\right) \\ & \frac{I_c}{I_o}=\frac{9}{8}\end{aligned}

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