Wave Motion as Inquiry by Fernando Espinoza

Author:Fernando Espinoza
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

For the first overtone L = 3/4 λ, and so the next harmonic is f = 3v/4 L = 3 f 1 or f 3 instead of f 2!

The same is true for the next overtone where L = 5/4 λ, and so its frequency is 5f 1 or f 5

Therefore, we can see that for a tube closed at one end the even harmonics are missing, only the odd ones appear. That is what makes a difference in the tone quality produced by wind instruments that are open at both ends (like a flute), and those reed instruments (like a clarinet) that are open at one end only.

Exercises

1.What is the length of a string that produces a second harmonic frequency of 300 Hz if its wavelength is 20 cm?

(Hint: this exercise can be solved either by getting the length from the equation for the second harmonic directly or by realizing that the second harmonic is simply twice the first, and then finding the length from the fundamental one).

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