What are the first three harmonics of a note produced on a 32.0 cm long violin string if waves on this string have a speed of 280.0 m/s? ___ Hz
___Hz
___Hz

The first harmonics are the fundamental, the first overtone, and the second overtone,

For a string fixed at both ends you have:

N-A-N            F/2

N-A-N-A-N     F

N-A-N-A-N-A-N    3 F/2        each harmonic increases by F/2

Where N are the anti-nodes and A the antinodes

N-A-N-A-N    represents 1 wavelength for string fixed at both ends

So 1 wavelength is 64 cm

280 m/s = F * .64 m       and F = 437.5 Hz       (second harmonic)

First harmonic = F/2 = 218.75 / sec

Third harmonic = 3 F / 2 = 656.25 /sec

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