Respuesta :
Answer:
Explanation:
Given
mass of string [tex]m=22\ gm[/tex]
Tension in the string [tex]T=23\ N[/tex]
Time taken by wave [tex]t=40\ ms[/tex]
We know velocity of wave is given by
[tex]v=\sqrt{\frac{T}{\mu }}[/tex]
where [tex]\mu =\frac{m}{L}[/tex]
[tex]v=\sqrt{\frac{TL}{m}}----1[/tex]
also velocity[tex]=\frac{L}{t}----2[/tex]
From 1 and 2 we get
[tex]\frac{L}{t}=\sqrt{\frac{T}{\mu }}[/tex]
[tex]L=\frac{Tt^2}{m}[/tex]
[tex]L=\frac{23\times (40\times 10^{-3})^2}{22\times 10^{-3}}[/tex]
[tex]L=1.67\ m[/tex]
The length of the string is 1.67 m
The speed of a wave is determined by the features of the medium in which the wave travel. The frequency of the sound generated is largely determined by the wave speed on the strings as well as the wavelength.
The wave speed of a stretched spring from the knowledge of linear density and tension can be expressed as:
[tex]\mathbf{v = \sqrt{\dfrac{T}{\mu}}}[/tex]
where;
- v = wave speed
- μ = linear density which can be expressed as [tex]\mathbf{\mu = \dfrac{m}{L}}[/tex]
- T = tensional force
The wave speed of the spring can be computed as:
[tex]\mathbf{v = \sqrt{\dfrac{TL}{m}}}[/tex]
Recall that:
the velocity of an object can also be expressed:
[tex]\mathbf{v = \dfrac{L}{t}}[/tex]
∴
Equating both above equations together, we have:
[tex]\mathbf{\dfrac{L}{t} = \sqrt{\dfrac{T}{\mu}}}[/tex]
By expressing length L the subject, we have:
[tex]\mathbf{L = \dfrac{T\times t^2}{m}}[/tex]
From the given information;
- The mass of string = 22 g
- The tensional force in the string = 23 N
- The length of the string is = unknown (???)
- The time duration = 40 ms = 0.04 s
[tex]\mathbf{L = \dfrac{ 23 \times (0.04)^2}{22 \times 10^{-3}}}[/tex]
L = 1.67 m
Therefore, we can conclude that the length of the string is 1.67 m
Learn more about the speed of a wave here:
https://brainly.com/question/10715783?referrer=searchResults
