Answer :
Final answer:
The fundamental frequency of the vibrating string attached to a 4 kg mass is calculated to be 15.64 Hz. The tension in the string is equivalent to the weight of the hanging object and the speed of the wave in the string is calculated using the tension and linear density.
Explanation:
To calculate the fundamental frequency of the vibrating string attached to a mass, you would first need to calculate the tension in the string, which, in this case, is equivalent to the weight of the hanging object. The formula for tension (T) is m*g, in which m=4 kg (mass of hanging object) and g=9.8 m/s^2 (gravity acceleration). This will result in a tension of 39.2 N.
Next, calculate the linear mass density of the string, written as μ = m/L, in which m=0.008 kg (mass of string) and L = 5 m (length of string). This gives a μ of 0.0016 kg/m.
The speed, (V) of the wave in the string is calculated using V = √(T/μ), resulting in V = √(39.2/0.0016) = √24500 ≈ 156.4 m/s.
Lastly, the fundamental frequency, usually denoted as f, can be calculated by the formula f = V/2L. Substituting the previously calculated value of V (156.4 m/s) and the length of the string (5 m), we get f = 156.4/10 = 15.64 Hz.
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Answer:
f = [ 1/ 2L] √ [ T /u]
u is the mass per unit length.
u = 0.008 kg / 5m= 0.0016 kg/m
T/u = 39.24 / 0.0016 =24525
√ [ T /u] = 156.61
f = [ 1/ 2L] √ [ T /u] = [1/ 2*5 ] *156.61
f = 15.66 Hz
