The tension in a 2.8-m-long, 1.2-cm-diameter steel cable (ρ = 7800 kg/m3) is 825 N. What is the fundamental frequency of vibration of the cable?
Fundamental wavelength = 5.6 m
V = Wave speed = sqrt(T/(ñ*A))
T = tension = 825 N
A = pi*d^2/4 = cross sectional area of cable
d = 0.012 m
Solve for V. Then use
Fundamental frequency
= V/(Fund. Wavelength)
thanks! but whats ñ
That was supposed to be your density symbol, rho. I never know what Greekm (or Spanish) symbols are going to pop up when I cut and paste.
thanks! may I ask how you calculate the fundamental wavelength or is it a constant?
calculated**
To find the fundamental frequency of vibration of the cable, we can use the following formula:
f = (1/2L) * sqrt(T/μ)
Where:
f = fundamental frequency of vibration
L = length of the cable
T = tension in the cable
μ = linear mass density of the cable
First, we need to calculate the linear mass density (μ) of the cable using the formula:
μ = ρ * A
Where:
ρ = density of the steel cable
A = cross-sectional area of the cable
To find the cross-sectional area (A) of the cable, we need to use the formula:
A = π * r^2
Where:
r = radius of the cable
Given information:
L = 2.8 m
Diameter (d) = 1.2 cm
ρ = 7800 kg/m^3
To find the radius (r), we need to convert the diameter from centimeters to meters:
d = 1.2 cm = 0.012 m
Now we can calculate the radius (r):
r = d/2 = 0.012 m / 2 = 0.006 m
Next, we can calculate the cross-sectional area (A):
A = π * r^2 = π * (0.006 m)^2 = 0.000113 m^2
Now we can calculate the linear mass density (μ):
μ = ρ * A = 7800 kg/m^3 * 0.000113 m^2 = 0.88 kg/m
Finally, we can calculate the fundamental frequency (f):
f = (1/2L) * sqrt(T/μ) = (1 / (2 * 2.8 m)) * sqrt(825 N / 0.88 kg/m) = (1 / 5.6 m) * sqrt(937.5 N/kg) = 0.179 Hz
Therefore, the fundamental frequency of vibration of the cable is approximately 0.179 Hz.