Question

A cellist tunes the C string of her instrument to a fundamental frequency of 65.4 Hz . The vibrating portion of the string is 0.600 m long and has a mass of 14.4 g .
What is μ, the mass per unit length of the string?
To determine the wave speed from purely kinematic quantities, you need to know the wavelength of the wave. What is the wavelength λ of the fundamental mode in the C string of the cello?

Answer 1

Explanation:

Given that,

Fundamental frequency of the string, f = 65.4 Hz

Length of the string, l = 0.6 m

Mass, m = 14.4 g = 0.0144 kg

(a) Let $\mu$ is the mass per unit length of the string. It can be calculated as :

$\mu=\dfrac{m}{l}$

$\mu=\dfrac{0.0144\ kg}{0.6\ m}$

$\mu=0.024\ kg/m$

(b) If f is the fundamental frequency of the string, the wavelength of the fundamental mode is given by :

$l=\dfrac{n\lambda}{2}$

$\lambda=\dfrac{2l}{n}$

n = 1        

$\lambda=2l=2\times 0.6\ m$

$\lambda=1.2\ m$

Hence, this is the required solution.