Why Does the Second Harmonic Frequency Double in a Fixed Rope?

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SUMMARY

The second harmonic frequency of a rope fixed at both ends is double that of the fundamental frequency. Given a fundamental frequency of 30Hz, the second harmonic frequency is 60Hz. This occurs because the second harmonic consists of two loops, resulting in a wavelength that is half that of the fundamental mode, which contains one loop. The relationship between frequency and wavelength is defined by the equation v = f * wavelength.

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Homework Statement



If the fundamental frequency for a rope fixed at both ends is 30Hz, what is the frequency of the second harmonic?


Homework Equations



v=f*wavelength



The Attempt at a Solution



correct answer is 60Hz. Can somebody please explain? Thank you.
 
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In the fundamental mode of vibration, the rope contains one loop which is λ/2. In the second harmonic the number of loops are two. Then what is the new wavelength?
 

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