For a certain orgas pipe, three succes ssive resonance frequencies are observed ol 425, 595 and 765 Hz respectively. Thking the speed of sound in air to be 340 m/s
(a) Explain whether the pipe is closed at one end or open at both ends
b) Determine the fundamental frequency and length of the pipe.

Explanation

The given frequencies are in the ratio 425 : 595 : 765, i.e., 5:7:9 and as clearly these are odd integers so the given pipe is closed at one end.
(b) From part (a) it is clear that the frequency of 5th harmonic (which is 2nd overtone) is
`425 Hz. So 425 = 5f_(c)= or f_(c)=85 Hz`.
Further as `f_(c)=(v)/(4L),L=(v)/(4f_(c))=(340)/(4xx85)=1m`