A 100.0 meter long transmission cable is suspended between two towers. If the mass density is 2.00 kg/m and the tension in the cable is , what is the speed in m/s of waves on the cable?
To determine the speed of waves on the cable, we can use the wave speed formula:
wave speed (v) = square root of (tension (T) / linear mass density (μ))
Given:
Length of the cable (L) = 100.0 m
Mass density (μ) = 2.00 kg/m
Tension in the cable (T) = (missing value)
We need to find the tension in the cable in order to calculate the wave speed.
To find the tension, we can use the relationship between tension, mass density, and gravity:
Tension (T) = (mass density (μ) x gravitational acceleration (g) x length of the cable (L))
The gravitational acceleration (g) is approximately 9.8 m/s^2.
Substituting the known values, we have:
Tension (T) = (2.00 kg/m x 9.8 m/s^2 x 100.0 m)
Calculating the tension:
Tension (T) = 1960 N
Now that we have the tension, we can calculate the speed of waves on the cable by using the wave speed formula:
wave speed (v) = square root of (tension (T) / linear mass density (μ))
Substituting the known values:
wave speed (v) = square root of (1960 N / 2.00 kg/m)
Calculating the wave speed:
wave speed (v) = square root of (980 m^2/s^2 / 2.00 kg/m)
wave speed (v) = square root of 490 m^2/s^2
wave speed (v) ≈ 22.1 m/s
Therefore, the speed of waves on the cable is approximately 22.1 m/s.