You visited us 7 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Standing Waves in Closed Organ Pipe

An organ pipe...

Question

An organ pipe $P_{1}$ closed at one end and vibrating in its first overtone pipe $P_{2}$ open at booth ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of the lengths of $P_{1}$ to that of $P_{2}$ is

3/8

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1/3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1/2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

8/3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B 3/8
First overtone of closed organ pipe:
$\frac{3 λ}{4} = L_{1}$

$f_{1} = \frac{v}{λ_{1}} = \frac{3 v}{4 L_{1}}$

Third overtone of open organ pipe:

$\frac{4 λ}{2} = L_{2}$

$f_{2} = \frac{v}{λ_{2}} = \frac{2 v}{L_{2}}$

Given $f_{1} = f_{2}$

$\frac{3 v}{4 L_{1}}$ $= \frac{2 v}{L_{2}}$

$\Rightarrow \frac{L_{1}}{L_{2}} = \frac{3}{8}$

Suggest Corrections

Similar questions

Q. An organ pipe

P_{1}

closed at one end is vibrating in its first overtone and another organ pipe

P_{2}

opened at both ends is vibrating in its third overtone are in resonance with a given tuning fork. The ratio of length of organ pipe

P_{1}

and

P_{2}

An organ pipe $P_{1}$ closed at one end vibrating in its first overtone and another pipe $P_{2}$ open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of $P_{1}$ and P2 is

[EAMCET 1997; MH CET 1999; AFMC 2001]

Q. An organ pipe

P_{1}

closed at one end and vibrating its third harmonic, and another pipe

P_{2}

, open at both ends and vibrating in its fourth harmonic, are in resonance with a given turning fork. The ratio of the length of

P_{1}

to that of

P_{2}

is:

Q. An organ pipe

P_{1}

closed at one end vibrating in its first harmonic and pipe

P_{2}

open at both ends vibrating in its third harmonic are in resonance with the same tuning fork. The ratio of their lengths is

Q. The first overtone of a closed pipe

P_{1}

and third over-tone of an open pipe

p_{2}

are in resonance with a tuning fork. The ratio of the length of the pipes

p_{1}

and

p_{2}

are

Join BYJU'S Learning Program

An organ pipe P1 closed at one end and vibrating in its first overtone pipe P2 open at booth ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of the lengths of P1 to that of P2 is

The correct option is B 3/8First overtone of closed organ pipe:3λ4=L1f1=vλ1=3v4L1Third overtone of open organ pipe:4λ2=L2f2=vλ2=2vL2Given f1=f23v4L1 =2vL2⇒L1L2=38

An organ pipe $P_{1}$ closed at one end and vibrating in its first overtone pipe $P_{2}$ open at booth ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of the lengths of $P_{1}$ to that of $P_{2}$ is