The third overtone of an open organ pipe of length lo has the same frequency as the third overtone of a closed pipe of length lc. The ratio (lo/lc) is equal to

Question

The third overtone of an open organ pipe of length lo has the same frequency as the third overtone of a closed pipe of length lc. The ratio (lo/lc) is equal to (A) 2 (B) (3/2) (C) (5/3) (D) (8/7)

Tardigrade Admin · Accepted Answer

The frequency of the third overtone (or fourth harmonic) of an open pipe of length

l_{o}

is

υ_{o} = \frac{4 v}{2 l _{o}}

The frequency of the third overtone (or seven harmonic) of a closed pipe of length

l_{c}

is

υ_{c} = \frac{7 v}{4 l _{c}}

As per question

υ_{o} = υ_{c}

∴ \frac{4 v}{2 l _{o}} = \frac{7 v}{4 l _{c}}

or

\frac{l _{o}}{l _{c}} = \frac{8}{7}

Q. The third overtone of an open organ pipe of length $l_{o}$ has the same frequency as the third overtone of a closed pipe of length $l_{c}$ . The ratio $\frac{l _{o}}{l _{c}}$ is equal to

2

$\frac{3}{2}$

$\frac{5}{3}$

$\frac{8}{7}$

Q. The third overtone of an open organ pipe of length lo​ has the same frequency as the third overtone of a closed pipe of length lc​. The ratio lc​lo​​ is equal to

2

23​

35​

78​

Q. The third overtone of an open organ pipe of length $l_{o}$ has the same frequency as the third overtone of a closed pipe of length $l_{c}$ . The ratio $\frac{l _{o}}{l _{c}}$ is equal to

$\frac{3}{2}$

$\frac{5}{3}$

$\frac{8}{7}$