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$\cdot$ With what tension must a rope with length 2.50 $\mathrm{m}$ and mass0.120 $\mathrm{kg}$ be stretched for transverse waves of frequency 40.0 $\mathrm{Hz}$to have a wavelength of 0.750 $\mathrm{m} ?$

$F=43.2 \mathrm{N}$

Physics 101 Mechanics

Chapter 12

Mechanical Waves and Sound

Periodic Motion

Mechanical Waves

Sound and Hearing

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so we want the tension in the rope. We know that the velocity is going to be equal to the square root of the force. Tension divided by mu. The linear density, linear densities simply defined as thie mass divided by the length S O. We're going to say that the velocity is also equal to the wavelength multiplied by the frequency. So we can say that the force tension there's going to be equal to mu. The linear density times v squared. So we can say that the fourth tension is going to be equal. Teo Mass times Lambda Times Frequency squared, divided by the length. And this is giving us points. 1 to 0 kilograms, times 40 hurts and then times the wavelength of 0.75 meters. This entire term is squared and then this is divided by the length of 2.50 meters and we get a force tension equal to 43 point to Newton's. So this would be our final answer. That is the end of the solution. Thank you for watching

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