A stretched wire of length 1.0 m is clamped at both ends. It is plucked at its center as shown. The three longest wavelengths in the wire are (in meters):
A) 4, 2, 1
B) 2, 1, 0.5
C) 2, 0.67, 0.4
D) 1, 0.5, 0.33
E) 1, 0.67, 0.5

Question

A stretched wire of length 1.0 m is clamped at both ends. It is plucked at its center as shown. The three longest wavelengths in the wire are (in meters): 
A) 4, 2, 1 
B) 2, 1, 0.5 
C) 2, 0.67, 0.4 
D) 1, 0.5, 0.33 
E) 1, 0.67, 0.5

Quizplus · Accepted Answer

The fundamental frequency of the wire corresponds to a wavelength equal to twice the length of the wire, which is 2.0 m. The next longest wavelength is 2/3 of the length of the wire, or 0.67 m. The next one is 2/5 of the length of the wire, or 0.4 m. Therefore, the answer is C, which has the closest values to 2.0, 0.67, and 0.4.

A Stretched Wire of Length 1