A guitar string 61.8 cm long vibrates with a standing wave that has three antinodes. Which harmonic is this?
third
To determine the harmonic of a standing wave on a guitar string, we need to understand the relationship between the length of the string and the number of antinodes.
A standing wave on a string has nodes and antinodes. A node is a point on the string where the amplitude of the wave is zero, while an antinode is a point on the string where the amplitude is at its maximum.
In the case of a guitar string, the fundamental frequency (first harmonic) produces one antinode, and the length of the string is equal to half the wavelength of the wave. Each subsequent harmonic (higher frequency) adds one additional node and one additional antinode.
We are given that the guitar string is 61.8 cm long and has three antinodes. This means that there are two nodes (one more than the number of antinodes).
Since each harmonic adds one additional node and one additional antinode, we can conclude that the standing wave on this string represents the third harmonic.
To calculate the length of the string for the fundamental frequency, we divide the length of the string by the number of antinodes (3 - 1 = 2) and multiply the result by the wavelength of the fundamental frequency. However, this is already given in the question, so we don't need to calculate it in this case.