To determine the tension required for waves to travel on a string at a specific speed, we can use the wave equation:
v = √(T/μ)
where: v is the wave speed, T is the tension in the string, and μ (mu) is the linear mass density of the string.
The linear mass density (μ) is calculated by dividing the mass of the string (m) by its length (L):
μ = m/L
Given: Mass of the string (m) = 0.010 kg Length of the string (L) = 2.50 m Wave speed (v) = 125 m/s
First, let's calculate the linear mass density (μ):
μ = m/L = 0.010 kg / 2.50 m = 0.004 kg/m
Now we can rearrange the wave equation to solve for tension (T):
T = μ * v^2
T = 0.004 kg/m * (125 m/s)^2
T = 0.004 kg/m * 15625 m^2/s^2
T = 62.5 N
Therefore, the tension required for waves to travel on the string at a speed of 125 m/s is 62.5 Newtons.