Respuesta :
The ratio of the masses of the two ropes (m1/m2) is 0.51.
The square root of the tension divided by the mass per length, or the linear density determines the speed of a wave on a string.
The formula used to relate the speed of a pulse on the rope (the speed of a wave on a string under tension) is given by |v| = √(F/μ) where v is the speed of a wave, F is tension in the string/rope, and μ is linear density (μ=m(mass)/L(length)).
Then, the speed of pulse on the first rope is, v₁ = √(F/μ₁). Given v₁ is 1.4 times v₂. Therefore, 1.4 v₂ = √(F/μ₁).
The speed of pulse on the second rope is, v₂ = √(F/μ₂). Substitute this value in the previous equation, and we get,
1.4√(F/μ₂) = √(F/μ₁)
Squaring on both sides of this equation,
[tex]\begin{aligned}1.96\left(\frac{F}{\mu_2}\right)&=\frac{F}{\mu_1}\\\frac{\mu_1}{\mu_2}&=\frac{1}{1.96}\\\frac{\frac{m_1}{L}}{\frac{m_2}{L}}&=\frac{1}{1.96}\\\frac{m_1}{m_2}&=0.510\end{aligned}[/tex]
The answer is 0.51.
To know more about the speed of a wave:
https://brainly.com/question/15055277
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