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

Question

An organ pipe P1 closed at one vibrating in its first overtone and another pipe P2 open at both ends vibrating in third overtone are in resonance with a given tuning fork. The ratio of the length of P1 to that of P2 is (A) 8/3 (B) 3/8 (C) 1/2 (D) 1/3

Tardigrade Admin · Accepted Answer

3 × (v/4 lc)=4 × (v/2 l o) or (lc/l o)=(3 v/4) × (2/4 v) =(3/8)

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

8/3

3/8

1/2

1/3

$3 \times \frac{v}{4 l _{c}} = 4 \times \frac{v}{2 l o}$
or $\frac{l _{c}}{l o} = \frac{3 v}{4} \times \frac{2}{4 v}$
$= \frac{3}{8}$

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

8/3

3/8

1/2

1/3

3×4lc​v​=4×2lov​ or lolc​​=43v​×4v2​ =83​

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

$3 \times \frac{v}{4 l _{c}} = 4 \times \frac{v}{2 l o}$
or $\frac{l _{c}}{l o} = \frac{3 v}{4} \times \frac{2}{4 v}$
$= \frac{3}{8}$