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  4. A pipe open at both the ends produces a note of fundamental frequency f1 . When the pipe is kept with (3/4) th of its length in water, it produces a note of fundamental frequency f2 . The ratio of (f1/f2) is:

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Q. A pipe open at both the ends produces a note of fundamental frequency $ {{f}_{1}} $ . When the pipe is kept with $ \frac{3}{4} $ th of its length in water, it produces a note of fundamental frequency $ {{f}_{2}} $ . The ratio of $ \frac{{{f}_{1}}}{{{f}_{2}}} $ is:

KEAMKEAM 2004

Solution:

Accordingly, $ {{f}_{1}}=\frac{v}{2l} $ .. (1)
and $ {{f}_{2}}=\frac{v}{4l/4}=\frac{v}{l} $ .. (2)
Hence, $ \frac{{{f}_{1}}}{{{f}_{2}}}=\frac{1}{2} $