Two organ pipes are made of the same material and are kept at 20 °C where the speed of sound is 343 m s⁻¹. One pipe is closed at one end while the other is open at both ends. Both pipes are adjusted so that they produce exactly the same fundamental frequency.
(i) Derive an expression connecting the lengths of the two pipes under this condition.
(ii) If the closed pipe has a length of 0.75 m, calculate the length of the open pipe.
(iii) On a hot afternoon the speed of sound rises by 2 %. Determine the new frequencies of the first overtone for each pipe.