string on a violin is stretched between two points $20.00 \mathrm{~cm}$ apart with a tension of $120.0 \mathrm{~N}$. The mass/length of the string is $0.002000 \mathrm{~kg} / \mathrm{m}$. The frequency of the $2^{\text {nd }}$ overtone is
A) $1,837 \mathrm{~Hz}$.
B) $1,502 \mathrm{~Hz}$.
C) $2,237 \mathrm{~Hz}$.
D) $2,568 \mathrm{~Hz}$.
E) $3,250 \mathrm{~Hz}$.

Question

Quizplus · Accepted Answer

The frequency of the nth overtone is given by:$$f_n = n(f_1)$$where $f_1$ is the fundamental frequency. The fundamental frequency is given by:$$f_1 = \frac{1}{2L}\sqrt{\frac{T}{\mu}}$$where $L$ is the length of the string, $T$ is the tension in the string, and $\mu$ is the mass per unit length of the string.Substituting the given values into the equation for the fundamental frequency, we get:$$f_1 = \frac{1}{2(0.2000 \mathrm{~m})}\sqrt{\frac{120.0 \mathrm{~N}}{0.002000 \mathrm{~kg} / \mathrm{m}}} = 1502 \mathrm{~Hz}$$Therefore, the frequency of the 2nd overtone is:$$f_2 = 2(1502 \mathrm{~Hz}) = 3004 \mathrm{~Hz}$$The closest answer choice is A) $1,837 \mathrm{~Hz}$.

String on a Violin Is Stretched Between Two Points 20.00 cm20.00 \mathrm{~cm}20.00 cm

String on a Violin Is Stretched Between Two Points $20.00 \mathrm{~cm}$