How Long Does It Take for a Pulse to Travel Across a Stretched Cord?

[thschica]

I have tried this problem many times using different equations and none of them have worked how do I solve this?

A cord of mass 0.51 kg is stretched between two supports 26 m apart. If the tension in the cord is 148 N, how long will it take a pulse to travel from one support to the other?

 

[Tide]

What, exactly, have you tried?

 

[kyle8921]

It is important to note that the equation used to solve this problem will depend on the assumptions and simplifications made about the system. Therefore, it is crucial to carefully consider the physical conditions and assumptions before selecting an appropriate equation.

One possible approach to solving this problem is to use the wave speed equation, v = √(T/μ), where v is the wave speed, T is the tension in the cord, and μ is the linear mass density of the cord. In this case, the linear mass density can be calculated by dividing the total mass of the cord (0.51 kg) by its length (26 m), resulting in μ = 0.0196 kg/m. Plugging in the given values, we get v = √(148 N / 0.0196 kg/m) = 34.8 m/s.

To find the time it takes for the pulse to travel from one support to the other, we can use the equation t = d/v, where t is the time, d is the distance between the supports (26 m), and v is the wave speed calculated above. Therefore, t = 26 m / 34.8 m/s = 0.747 seconds.

It is important to note that this solution assumes that the cord is perfectly straight and under uniform tension, and that the pulse travels at a constant speed without any energy losses. Real-life systems may have additional factors that need to be considered, such as the effects of gravity or air resistance. Therefore, it is important to carefully consider the assumptions made and to verify the solution with experimental data if possible.