A cord of mass 0.58 kg is stretched between two supports 28.1 m apart. If the tension in the cord is 273 N, how long will it take a pulse to travel from one support to the other?
To find out how long it will take a pulse to travel from one support to the other, we need to determine the speed of the pulse on the cord.
The speed of a wave on a string is given by v = √(T/μ), where v is the speed of the wave, T is the tension in the cord, and μ is the linear mass density of the cord.
The linear mass density (μ) is calculated by dividing the mass of the cord (m) by its length (L). In this case, the mass of the cord is 0.58 kg, and the length is 28.1 m. So, μ = m/L = 0.58 kg / 28.1 m = 0.02064 kg/m.
Using the given tension of 273 N and the linear mass density of 0.02064 kg/m, we can now determine the speed of the pulse:
v = √(T/μ) = √(273 N / 0.02064 kg/m) = √(13233.44 m^2/s^2) = 115.05 m/s.
Finally, 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, and v is the speed of the pulse. Plugging in the values, we have:
t = 28.1 m / 115.05 m/s = 0.244 s.
Therefore, it will take approximately 0.244 seconds for the pulse to travel from one support to the other.