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If you take 42.0 meters of string and ball it up and put it on a scale you measure that it weighs 18.8 grams. If you tighten a length of this same string to a tension of 8.5 Newtons, what is the wave speed for waves that would travel on this string when you plucked it?

Respuesta :

Answer:

137.74 m/s

Explanation:

[tex]L[/tex] = length of the string = 42 m

[tex]m[/tex]  = mass of the string = 18.8 g = 0.0188 kg

Linear mass density is given as

[tex]\mu =\frac{m}{L}[/tex]

[tex]\mu =\frac{0.0188}{42}[/tex]

[tex]\mu[/tex]  = 0.000448 kg/m

[tex]v[/tex]  = wave speed

[tex]T[/tex]  = Tension force in the string = 8.5 N

Wave speed is given as

[tex]v = \sqrt{\frac{T}{\mu }}[/tex]

[tex]v = \sqrt{\frac{8.5}{0.000448 }}[/tex]

[tex]v[/tex]  = 137.74 m/s

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