Explanation:
Formula for the organ pipe of length L which is open at both the ends. So, its third harmonic frequency will be given as follows.
[tex]f_{3} = 3(\frac{v}{2L})[/tex]
where, v = speed of the sound = 344 m/s
[tex]f_{3}[/tex] = 392 Hz
Hence, putting the given values into the above formula as follows.
[tex]f_{3} = 3(\frac{v}{2L})[/tex]
L = [tex]\frac{3v}{2f_{3}}[/tex]
= [tex]\frac{3 \times 344}{2 \times 392}[/tex]
= [tex]\frac{1032}{784}[/tex]
= 1.316 m
Thus, we can conclude that the length of the pipe is 1.316 m.
