Question

An organ pipe open at both ends has two successive harmonics with frequencies of 220 Hz and 240 Hz. What is the length of the pipe? The speed of sound is 343 m/s in air.

Answer 1

Answer:

The  value is  $l = 8.58 \ m$

Explanation:

From the question we are told that

  The  frequencies of two successive harmonics  is  $f_ a = 220 \ Hz$ , $f_b = 240 \ Hz$

   The  speed of sound in the air is  $v = 343 \ m/s$

Generally a harmonic frequency is mathematically represented as

        $f_n = \frac{n * v }{2l}$

here l is the length of the pipe

n is the order of position of the harmonics

 Now since we do not know the order of the given harmonic frequencies but we are told that they are successive then the frequencies can be mathematically represented as

     $220 = \frac{n * v}{ 2 l }$

and

     $240 = \frac{ (n+1 ) v }{2l}$

So  

    $240 - 220 = \frac{ (n+1 ) v }{2l} - \frac{n * v}{ 2 l }$

   $20 = \frac{v}{2l}$

=>   $l = 8.58 \ m$