Two strings on a violin are stretched between two points 20 cm apart.The tensions of the strings are the same.If the ratio of the frequencies of the fundamental modes is 1.5 to 1.0,then what is the ratio of the mass per lengths in the strings?
A) 0.80
B) 0.90
C) 0.85
D) 0.94
E) 0.78

Question

Quizplus · Accepted Answer

The frequency of a string is given by:f = (1/2L) * sqrt(T/m)where L is the length of the string, T is the tension, and m is the mass per length.If the tensions are the same, then the ratio of the frequencies is:f1/f2 = sqrt(m2/m1)where m1 and m2 are the mass per lengths of the strings.If the ratio of the frequencies is 1.5 to 1.0, then:1.5 = sqrt(m2/m1)m2/m1 = 2.25m2 = 2.25 * m1Therefore, the ratio of the mass per lengths in the strings is 2.25 to 1.0, which is closest to choice A) 0.80.

Two Strings on a Violin Are Stretched Between Two Points