Final answer:
The tension in a string with a mass of 0.83 kg and length 12.29 m, where waves travel at 28.5 m/s, is approximately 54.91 Newtons.
Step-by-step explanation:
The tension in a string through which waves are traveling can be determined using the wave speed, the string's mass, and its length, which gives us the linear mass density of the string. Here, we're given a string of mass 0.83 kg and length 12.29 m, and waves travel along the string at 28.5 m/s. To find the tension, we first need to calculate the string's linear mass density (μ), which is the mass per unit length.
The linear mass density (μ) is: μ = (mass of string)/(length of string) = 0.83 kg / 12.29 m ≈ 0.0675 kg/m.
Using the formula for wave speed on a string, v = √(T/μ), and solving for T (tension), we get: T = μv². Substituting the given values, T = 0.0675 kg/m * (28.5 m/s)² ≈ 54.91 N. Hence, the tension in the string is approximately 54.91 Newtons.