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) = y 1 (x, t) + y 2 (x, t)
where
y 1 (x, t) = C sin ω 1 t sin k 1 x
y 2 (x, t) = C sin ω 2 t sin k 2 x
with ω 1 = vk 1 and ω 2 = vk 2 .
f 1 , t = 
f 1 , t = 
f 1 , and t = 
f 1 .
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
The fundamental has nodes only at the ends, x = 0 and x = L.
For the second harmonic, the wavelength is the length of the string, and the nodes are at x = 0, x = L/2 and x = L.
No; no part of the string except for x = L/2, oscillates with a single frequency.
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