Respuesta :
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 [tex]\mu[/tex] is the mass per unit length of the string. It can be calculated as :
[tex]\mu=\dfrac{m}{l}[/tex]
[tex]\mu=\dfrac{0.0144\ kg}{0.6\ m}[/tex]
[tex]\mu=0.024\ kg/m[/tex]
(b) If f is the fundamental frequency of the string, the wavelength of the fundamental mode is given by :
[tex]l=\dfrac{n\lambda}{2}[/tex]
[tex]\lambda=\dfrac{2l}{n}[/tex]
n = 1
[tex]\lambda=2l=2\times 0.6\ m[/tex]
[tex]\lambda=1.2\ m[/tex]
Hence, this is the required solution.
The mass per unit length of the string is 0.024 kg/m, and the wavelength is 1.2 meters.
What is the frequency?
It is defined as the number of waves that crosses a fixed point in one second known as frequency. The unit of frequency is per second.
We have:
Fundamental frequency = 65.4 Hz
Length of the vibrating string portion = 0.6 meter
Mass of the vibrating string portion = 144 grams
We know the formula for mass per unit length:
[tex]\rm \mu = \frac{m}{l}[/tex]
[tex]=\rm \frac{0.0144 \ kg}{0.6 \ meter}[/tex] ( m = 144 grams ⇒ 0.0144 kg)
[tex]\rm \mu = 0.024 \ kg/m[/tex]
The wavelength of the fundamental mode is given by:
[tex]\rm l =\frac{n\lambda}{2}[/tex]
[tex]\rm \lambda = \frac{2l}{n}[/tex]
[tex]\rm \lambda = 2\times 0.6 \Rightarrow 1.2 meter[/tex] (n = 1)
Thus, the mass per unit length of the string is 0.024 kg/m, and the wavelength is 1.2 meters.
Learn more about the frequency here:
https://brainly.com/question/27063800
