The fundamental (or first harmonic) standing wave represents the longest possibl

Question

The fundamental (or first harmonic) standing wave represents the longest possible wavelength standing wave that fits on the string. You identified the shape of it in the first part of this problem. It also represents the lowest possible frequency wave. One half wavelength fits on the string. If the string is 0.600 m long and the length of the string is equal to one half wavelength, what is the wavelength of the fundamental harmonic?

So how about the third harmonic. Think about what that looks like. Three half wavelengths fit on the string. If the string is 0.600 m long and the length of the string is equal to three half wavelengths, what is the wavelength of the third harmonic?

The frequency of the harmonics following a fairly simple pattern, as described in the text. If the frequency of the fundamental (n=1) harmonic is 80.0 Hz, what is the frequency of the second harmonic(n=2)?

If the frequency of the fundamental (n=1) harmonic is 80.0 Hz, what is the frequency of the third harmonic(n=3)?

Explanation / Answer

The wavelength will be:

lambda = 2 L = 2 x 0.6 = 1.2 m

Hence, lambda = 1.2 m

lambda(3) = 2 x L/3 = 2 x 0.6/3 = 0.4 m

Hence, lambda(3) = 0.4 m

the frequency of the 2nd harmonic will be:

f2 = 2f1 = 2 x 80 = 160 Hz

Hence, f2 = 160 Hz

the frequency of the 3rd harmonic will be:

f3 = 3 f1 = 3 x 80 = 240 Hz

Hence, f3 = 240 Hz

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