Question

A guitar string is vibrating in the third harmonic. The number of nodes and antinodes present are:

• A. 3 nodes, 2 antinodes
• B. 4 nodes, 3 antinodes
• C. 2 nodes, 3 antinodes
• D. 3 nodes, 4 antinodes

Hint:

In the \( n \)-th harmonic of a vibrating string, the number of nodes is \( n + 1 \), and the number of antinodes is \( n \).

Answer 1

The Correct Option is B

For a string vibrating in the third harmonic (n = 3), the number of nodes and antinodes can be determined using the following relationships: - The number of nodes in the third harmonic is \( n + 1 \), where \( n \) is the harmonic number. - The number of antinodes is \( n \). Thus, for the third harmonic: - Number of nodes = \( 3 + 1 = 4 \), - Number of antinodes = \( 3 \). Therefore, the correct answer is: \[ \boxed{(B) \, 4 \, \text{nodes,} \, 3 \, \text{antinodes}} \]