A guitar string of length L is plucked in such a way that the total wave produced is the sum of the fundamental and the second harmonic. That is, the standing wave is given by y(x, t) = y₁(x, t) + y₂(x, t), where with ki y₁ (x, t) = A₁ sin(w₁t) sin(k₁x) y₂(x, t) = A₂ sin(w₂t) sin(k₂x) = and k₂ = 27. a) At what values of x are the nodes of y₁? b) At what values of x are the nodes of y2? c) At what values of x are the nodes of y?

Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter18: Superposition And Standing Waves
Section: Chapter Questions
Problem 22PQ
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A guitar string of length L is plucked in such a way that the total wave produced is the sum of
the fundamental and the second harmonic. That is, the standing wave is given by
y(x, t) = y₁(x, t) + y₂(x, t),
where
2π
with k₁ = and k2 = ²″ .
y₁(x, t)
A₁ sin(w₁t) sin(k₁x)
y2(x, t) = A₂ sin(w₂t) sin(k2x)
=
a) At what values of x are the nodes of y₁?
b) At what values of x are the nodes of y2?
c) At what values of x are the nodes of y?
Transcribed Image Text:A guitar string of length L is plucked in such a way that the total wave produced is the sum of the fundamental and the second harmonic. That is, the standing wave is given by y(x, t) = y₁(x, t) + y₂(x, t), where 2π with k₁ = and k2 = ²″ . y₁(x, t) A₁ sin(w₁t) sin(k₁x) y2(x, t) = A₂ sin(w₂t) sin(k2x) = a) At what values of x are the nodes of y₁? b) At what values of x are the nodes of y2? c) At what values of x are the nodes of y?
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