For sound waves, if the number of nodes for the 5^ th harmonic of an open-ended pipe is n and that for the 9^ th harmonic of the same pipe with one of its ends closed is m , the ratio n m is :

Step-by-step solution

For an open-ended pipe, the p^ th harmonic contains p nodes and p+1 antinodes. For the 5^ th harmonic of the open-ended pipe, the number of nodes is n = 5 . For a pipe closed at one end, only odd harmonics are present. The q^ th harmonic (where q is an odd integer) contains q+1 2 nodes and q+1 2 antinodes. For the 9^ th harmonic of the closed pipe, the number of nodes is m = 9+1 2 = 5 . The ratio of the number of nodes is n m = 5 5 = 1 .