Which of the following wavelengths could NOT be present as a harmonic on a 2 m long string?
A) 4 m
B) 2 m
C) 1 m
D) 0.89 m
E) 0.5 m

Question

Quizplus · Accepted Answer

The wavelength of a harmonic on a string must satisfy the condition:
wavelength = 2L/n
where L is the length of the string and n is an integer representing the harmonic number.

For a 2 m long string, the possible wavelengths (in meters) for harmonics are:
n=1: wavelength = 2L/1 = 4 m
n=2: wavelength = 2L/2 = 2 m
n=3: wavelength = 2L/3 = 1.33 m
n=4: wavelength = 2L/4 = 1 m
n=5: wavelength = 2L/5 = 0.8 m
n=6: wavelength = 2L/6 = 0.67 m
n=7: wavelength = 2L/7 = 0.57 m
n=8: wavelength = 2L/8 = 0.5 m

Therefore, the wavelength of 0.89 m cannot be present as a harmonic on a 2 m long string.

Which of the Following Wavelengths Could NOT Be Present as a Harmonic