If a closed organ pipe has the same third harmonic frequency as that of an open organ pipe, then their respective lengths are in the ratio

Question

If a closed organ pipe has the same third harmonic frequency as that of an open organ pipe, then their respective lengths are in the ratio (A) 1: 1 (B) 1: 2 (C) 1: 4 (D) 3: 4

Tardigrade Admin · Accepted Answer

Third harmonic beginarrayl ⇒ (3 v /4 l e)=(3 v /2 l o ) ⇒ ( I c / l o )=(2/4)=(1/2) endarray Hence, we get =1: 2

Q. If a closed organ pipe has the same third harmonic frequency as that of an open organ pipe, then their respective lengths are in the ratio

1 : 1

1 : 2

1 : 4

3 : 4

Third harmonic
$< b r / > < b r / >\Rightarrow \frac{3 v}{4 l _{e}} = \frac{3 v}{2 l _{o}} < b r / >\Rightarrow \frac{I _{c}}{l _{o}} = \frac{2}{4} = \frac{1}{2} < b r / > < b r / >$
Hence, we get
$< b r / >= 1 : 2 < b r / >$

Q. If a closed organ pipe has the same third harmonic frequency as that of an open organ pipe, then their respective lengths are in the ratio

1 : 1

1 : 2

1 : 4

3 : 4

Third harmonic <br/><br/>⇒4le​3v​=2lo​3v​<br/>⇒lo​Ic​​=42​=21​<br/>​<br/> Hence, we get <br/>=1:2<br/>

Third harmonic
$< b r / > < b r / >\Rightarrow \frac{3 v}{4 l _{e}} = \frac{3 v}{2 l _{o}} < b r / >\Rightarrow \frac{I _{c}}{l _{o}} = \frac{2}{4} = \frac{1}{2} < b r / > < b r / >$
Hence, we get
$< b r / >= 1 : 2 < b r / >$