# The frequency of the second overtone of a closed pipe is in unison with the third overtone of an open pipe other ratio of lengths of the pipe is (a) 10: 8 (b) 5: 8 (c) 7: 4 (d) 4: 7

Arun
25763 Points
2 years ago

3rd overtonr of closed = 2nd harmonic of open

$7\left [ \frac{V}{4l_{c}} \right ]= 2\left [ \frac{V}{l_{0}} \right ]$

$\frac{l_{c}}{l_{0}}= \frac{7}{4}$

Closed organ pipe -

A closed organ pipe is a cylindrical tube having an air colume with one end closed.

- wherein

Condition of constructive interference

$l=\left ( 2n+1 \right )\frac{\lambda }{4}$

Vikas TU
14149 Points
2 years ago
Third overtone of closed organ pipe means seventh harmonic. Given
(f7)closed=(f4)open
7(ν/4IC)=4(ν/2I0)
lC/l0=7/8