Two strings are respectively 1.00 m and 2.00 m long. Which of the following wavelengths, in meters, could represent harmonics present on both strings?
A) 0.800, 0.670, 0.500
B) 1.33, 1.00, 0.500
C) 2.00, 1.00, 0.500
D) 2.00, 1.33, 1.00
E) 4.00, 2.00, 1.00

Question

Quizplus · Accepted Answer

The wavelengths of the harmonics present on both strings must be the same. The fundamental mode for the 1.00 m string has a wavelength of 2.00 m, and the fundamental mode for the 2.00 m string has a wavelength of 4.00 m. Therefore, any common harmonics must have wavelengths that are integer divisors of both 2.00 m and 4.00 m. The only common divisors are 2.00 m and 1.00 m, so the harmonics must have wavelengths of 2.00 m, 1.00 m, or 0.500 m. The only choice that includes all three of these options is C.

Two Strings Are Respectively 1