When a sonometer wire vibrates in the third overtone, the number of antinodes and nodes formed on the wire are respectively

Step-by-step solution

A sonometer wire is fixed at both ends. For a string fixed at both ends, the n -th overtone corresponds to the (n+1) -th harmonic, which consists of n+1 loops. For the third overtone, n = 3 . Number of loops = 3 + 1 = 4 . Since each loop contains exactly one antinode, the number of antinodes is 4 . The number of nodes on a string fixed at both ends is always one more than the number of antinodes. Number of nodes = 4 + 1 = 5 . Thus, the number of antinodes and nodes are 4 and 5 respectively. Answer: 4, 5