A string with a length of 3.0 m has two adjacent resonances at frequencies 112 Hz and 140 Hz.
-Determine the wavelength of the 140 Hz resonance.
A)0.30 m
B)0.60 m
C)1.2 m
D)1.5 m
E)1.8 m

Question

Quizplus · Accepted Answer

Since the length of the string is 3.0 m, we can find the wavelength of a standing wave using the formula:
wavelength = (2 x length of string) / n
where n is the harmonic number (1 for the fundamental, 2 for the first overtone, 3 for the second overtone, etc.)

For the 112 Hz resonance:
wavelength = (2 x 3.0 m) / 1 = 6.0 m

For the 140 Hz resonance:
wavelength = (2 x 3.0 m) / 2 = 3.0 m

Therefore, the wavelength of the 140 Hz resonance is 3.0 m or 1.2 m per cycle (since the wave has two cycles within the length of the string). 
The best choice is C, 1.2 m.

A String with a Length of 3