Given below are two statements: Statement I: For an open organ pipe, the n^ th overtone always contains (n+1) displacement nodes. Statement II: For a pipe closed at one end, the n^ th harmonic (where n is an odd integer) always contains n displacement nodes. In the light of the above statements, choose the most appropriate answer from the options given below:

Step-by-step solution

Evaluate Statement I: For an open organ pipe, the n^ th overtone corresponds to the (n+1)^ th harmonic. The number of displacement nodes in the p^ th harmonic of an open pipe is p . Therefore, the (n+1)^ th harmonic contains (n+1) displacement nodes. Statement I is correct. Evaluate Statement II: For a pipe closed at one end, only odd harmonics are present. The n^ th harmonic (where n is an odd integer) contains n+1 2 displacement nodes, not n nodes. For example, the 3^ rd harmonic contains 3+1 2 = 2 displacement n