Question

The fundamental frequency of a closed pipe is 220 Hz. If 1/4th of the pipe is filled with water, the frequency of the 1st overtone of the pipe now is

• A. 220 Hz
• B. 440 Hz
• C. 880 Hz
• D. 1760 Hz

Answer 1

The correct option is C 880 Hz

Fundamental frequency of closed pipe $\frac{v}{4L}=220Hz$ ----(1)

When $1/4^{th}$ of pipe is filled with water, length of the pipe decreases to ${\frac{3}{4}}^{th}$ of length .

So, 1st overtone $f=3{\nu }_c=\frac{3v}{4\left(\frac{3L}{4}\right)}=\frac{v}{L}$

So, from (1):

1st overtone frequency $\frac{v}{L}=\frac{4\nu }{4L}=4\times 220Hz=880Hz$