String Resonance Frequencies

What are the three smaller frequencies at which the string resonates besides 250 Hz?

The string resonates at 250 Hz in its fourth harmonic, so the fundamental frequency is 62.5 Hz. The smaller resonance frequencies are the multiples of the fundamental frequency: 62.5 Hz, 125 Hz, and 187.5 Hz.

Explanation:

If the string resonates at 250 Hz in four loops, this indicates that it is at its fourth harmonic, which means the fundamental frequency (first harmonic) is 250 Hz / 4 = 62.5 Hz. The other harmonics will be multiples of the fundamental frequency. Therefore, the three smaller frequencies at which it will resonate are:
  • 1st Harmonic (Fundamental frequency): 62.5 Hz
  • 2nd Harmonic: 62.5 Hz x 2 = 125 Hz
  • 3rd Harmonic: 62.5 Hz x 3 = 187.5 Hz
The correct answer from the given options is A: 125 Hz, 62.5 Hz, 31.25 Hz.
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