For a certain organ pipe, three successive resonance frequencies are observed at 425, 595 and 765 Hz,…
For a certain organ pipe, three successive resonance frequencies are observed at 425, 595 and 765 Hz, respectively. Taking the speed of sound in air to be 340 ms -1. (i) Explain whether the pipe is closed at one end or open at both ends. (ii) Determine the fundamental frequency and length of the pipe.
Solution
Sol. (i) The given frequencies are in the ratio $5:7:9$. As the frequencies are odd multiples of 85 Hz, the pipe must be closed at one end.
(ii) Now, the fundamental frequency is the lowest one, i. e. 85 Hz.
$\therefore\;85=\dfrac{v}{4l}\Rightarrow l=\dfrac{340}{4\times 85}=1\ \mathrm{m}$
Answer: $1 \mathrm{m}$