(Standing waves in air columns) Two organ pipes are tuned to produce standing waves in air at the same temperature.
(i) Write the general expression for the frequency of the nth harmonic in (a) a pipe open at both ends and (b) a pipe closed at one end.
(ii) The two pipes produce the same fundamental frequency. Prove that the length of the closed pipe must be exactly twice the length of the open pipe.
(iii) Explain, with the aid of a suitable sketch, why only odd harmonics are produced in the closed pipe whereas all harmonics are produced in the open pipe.
a. (i) Write the expressions.
b. (ii) Prove the relationship between lengths.
c. (iii) Explain the occurrence of harmonics.