The fundamental frequency (in Hz) of an open pipe is 594 Hz. What is the fundamental frequency if one end is closed ?

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Solution

Fundamental frequency of an open organ pipe is given by ,
$f_{1} = v / 2 L$ ,
where $L =$ length of organ pipe ,
$v =$ speed of sound wave ,
so $594 = v / 2 L$ , ( given $f_{1} = 594 H z$ ) ,
now fundamental frequency of a closed pipe is given by ,
$f_{1}^{'} = v / 4 L = \frac{1}{2} . (\frac{v}{2 L}) = 594 / 2 = 297 H z$ ,

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The fundamental frequency (in Hz) of an open pipe is 594 Hz. What is the fundamental frequency if one end is closed ?

Fundamental frequency of an open organ pipe is given by , f1=v/2L ,where L= length of organ pipe , v= speed of sound wave ,so 594=v/2L , ( given f1=594Hz) ,now fundamental frequency of a closed pipe is given by , f′1=v/4L=12.(v2L)=594/2=297Hz ,