For a string fixed at both ends, with a fundamental frequency of 440Hz, can there be a harmonic when a wave of frequency 220Hz is sent across the string? my book says no, but I disagree; can't standing waves and hence harmonics exist when its 1/2 a wavelength?
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The 220Hz wave requires double the wavelength of the fundamental if the velocity is fixed, from $v=f\lambda$, however all harmonics have a wavelength equal to or smaller than the fundamental.
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answered Oct 25, 2021 at 9:57
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$\begingroup$ "however all harmonics have a wavelength equal to or smaller than the fundamental." but the first harmonic in the diagram (assuming the fundamental wavelength is the distance from both fixed ends) has 2x a wavelength of the fundamental wavelength.. $\endgroup$– seb ayeOct 26, 2021 at 11:45
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$\begingroup$ @seb aye hi, the term 'fundamental wavelength' is the distance for a full wave of the fundamental mode, i.e imagine we extended the red line of the top diagram until it looked like a complete wave. It would then look like the blue one of the second diagram, but would have a length twice the distance between the lines. That is, the wavelength of the fundamental is twice the distance between the lines. $\endgroup$ Oct 26, 2021 at 12:19