Answer :
Final answer:
To calculate the wavelength of the vibration wave, we use the tension of the cable and the frequency of the vibration along with a typical linear mass density value for steel cable to find the wave speed. With the speed and frequency, we can determine the wavelength using the formula λ = v/f.
Explanation:
The question presented involves calculating the wavelength of a vibrational wave created by a steel cable under tension, which has been set into vibration by the wind. To find the wavelength, we must connect the concepts of wave speed in the medium, frequency, and tension. The speed of a wave (v) on a string or cable is given by the formula: v = √(T/μ), where T is the tension in the cable and μ is the linear mass density. Once we have the speed, we can use the relationship between speed, frequency (f), and wavelength (λ), which is v = f * λ, to find the desired wavelength.
The student provides the tension (T = 1,172 N) and the frequency (f = 1.5 Hz) but does not provide the linear mass density. We will assume that the linear mass density (μ) for a typical steel cable (μ = 0.02 kg/m), allows for a realistic scenario. With these three pieces of information, we can solve for the speed of the wave:
v = √(1,172 N / 0.02 kg/m)
Once we know the speed, we can rearrange the wave equation to solve for wavelength (λ = v/f):
λ = v / 1.5 Hz
This calculation will yield the wavelength of the vibration wave generated by the steel cable when the wind causes it to vibrate.
