Answer to Question #168845 in Mechanics | Relativity for savannah reyna

Question

1.A cello string vibrates in its fundamental mode with a frequency of 157 1/s. The vibrating segment is 76.9 cm long and has a mass of 0.64 g. Find the tension in the string. Answer in units of N.

2.Find the frequency of the string when it vibrates in six segments. Answer in units of 1/s.

Answer 1

When the string vibrates in the lowest frequency mode , the length of string forms a standing wave where is $L=\dfrac{λ}{2}$

$L=\dfrac{λ}{2}$  so the fundamental harmonic wavelength is λ=2L=2(0.769m)

λ=2L=2(0.769m)

= 1.538m

=1.538m and the speed is

v= fλ= $(157s^{-1}\times 1.538)$

v = 241.466 m/s

Hence, from the tension equation,

$v^2 = \dfrac{T}{\mu}$

We know, $\mu = \dfrac{m}{L}$

Hence, T = $\dfrac{(241.466)^2\times 0.00064}{0.769}$

T = 48.52 N

b.) The frequency of the string when it vibrates in six segments = $6\times f_1$

= $6\times 157$

= $942 s^{-1}$