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  4. A pipe closed at one end and open at the other end, resonates with sound waves of frequency 135 Hz and also 165 Hz, but not with any wave of frequency intermediate between these two. Then the frequency of the fundamental note is

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Q. A pipe closed at one end and open at the other end, resonates with sound waves of frequency $135\, Hz$ and also $165\, Hz$, but not with any wave of frequency intermediate between these two. Then the frequency of the fundamental note is

Waves

Solution:

In a closed pipe, resonance frequency,
$v=(2 r=1) v / 4 l$
$=135$ and $165 .$
The lowest frequency must be highest common factor of 125 and 165, which is $15\, Hz$.