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

Question

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 (A) 30 Hz (B) 15 Hz (C) 60 Hz (D) 7.5 Hz

Tardigrade Admin · Accepted Answer

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.

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

30 Hz

15 Hz

60 Hz

7.5 Hz

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 $15 Hz$ .

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