Question

Organ pipe A, with both ends open, has a fundamental frequency of 475 Hz. The third harmonic of organ pipe B, with one end open, has the same frequency as the second harmonic of pipe A. Use 343 m/s for the speed of sound in air. How long are (a) pipe A and (b) pipe B?

Answer 1

Answer:

The length of organ pipe A is $L = 0.3611 \ m$

The length of organ pipe B is  $L_b = 0.2708 \ m$

Explanation:

From the question we are told that

    The fundamental frequency is  $f = 475 Hz$

     The speed of sound is  $v_s = 343 \ m/s$

The fundamental frequency of the organ pipe A  is mathematically represented as

        $f= \frac{v_s}{2 L}$

Where L is the length of  organ pipe

   Now  making L the subject

        $L = \frac{v_s}{2f}$

substituting values

        $L = \frac{343}{2 *475}$

        $L = 0.3611 \ m$

The second harmonic frequency of the  organ pipe A is mathematically represented as

       $f_2 = \frac{v_2}{L}$

The third harmonic frequency of the  organ pipe B is mathematically represented as      

      $f_3 = \frac{3 v_s}{4 L_b }$

So from the question

       $f_2 = f_3$

So

    $\frac{v_2}{L} = \frac{3 v_s}{4 L_b }$

Making  $L_b$ the subject

     $L_b = \frac{3}{4} L$

substituting values

    $L_b = \frac{3}{4} (0.3611)$

    $L_b = 0.2708 \ m$