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?

The length of organ pipe A is

The length of organ pipe B is  

Explanation:

From the question we are told that

    The fundamental frequency is  

     The speed of sound is  

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

Where L is the length of  organ pipe

   Now  making L the subject

substituting values

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

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

So from the question

So

Making   the subject

substituting values