Harmonic Wavelengths Of A String Fixed At Two Points Distance L Apart

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Harmonic Wavelengths Of A String Fixed At Two Points Distance L Apart

Sinusoids 1, 2 and 3 represent the first, second and third harmonics respectively, of a string fixed at two points distance L apart.

(a) Compare the octaves of 2 and 3 relative to 1.

(b)What is the harmonic wavelength of the fourth harmonic?

(c) What is the general equation that relates the harmonic wavelength of the string to the distance L, between the two fixed points?

**The strings**:
S_{7}P_{4}A_{44} (Motion - Oscillatory).
**The math**:

Pj Problem of Interest is of type *motion* (oscillatory).

(a) 2 is one octave above 1.

3 is a fifth above the octave.

(b) L/2

(c) In general, harmonic wavelength = λ_{n} = (2L)/n. n =1, 2, 3 ...

Math

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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