Question

A guitar string with a linear mass density of 2.0 g/m is stretched between two vertical rods that are 65 cm apart. The string holds a standing wave, fixed at both ends, with three antinodes when it oscillates at a frequency of 430 HzWhat is the frequency of the fifth harmonic of this string?

Answer 1

717 Hz

Step-by-step explanation:

solution:

The wave with three antinodes has m = 3. Thus, f_3 = 3f_1 and so the fundamental frequency of the string is

f_1 =f_3/3

=430 Hz/3

=143 Hz

Thus, the frequency of the fifth harmonic is

f_5 = 5*f_1

= 5*143 Hz

= 717 Hz