An open organ pipe is vibrating in its 3^ rd overtone. What is the ratio of the number of pressure nodes to the number of displacement nodes in this mode of vibration?

Step-by-step solution

For an open organ pipe, the n^ th overtone corresponds to the (n+1)^ th harmonic. The 3^ rd overtone is the 4^ th harmonic. In an open pipe, the p^ th harmonic has p displacement nodes and p+1 displacement antinodes. Thus, for the 4^ th harmonic, there are 4 displacement nodes and 5 displacement antinodes. In a standing sound wave, a displacement antinode corresponds to a pressure node (where pressure variation is zero). Therefore, the number of pressure nodes is equal to the number of displacement antinodes, which