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Answer:
a. radius = 0.0006m = 0.6mm and length =0.393m = 393mm
b. frequency =377.86Hz
Explanation:
Given:
mass of steel= 4g = 0.004kg
density of steel = 7890kg/m3
tensile stress of steel 7.0x10⁸
tension load =900N
from the density, we will calculate for the Volume of the steel string
density = mass/volume
volume = mass/density = 0.004/7890 = 5.07 x 10⁻⁷ m³
from the tensile stress will can get the maximum base Area of the string ,
tensile stress = load/area =
7x10⁸ = 900/A
A = 900/7x10⁸ = 1.29x10⁻⁶ m²
Area = πr²
area/pi = 4.105x10-7
radius = 0.0006m = 0.6mm
volume = Area x length
length = vol/area =(5.07 x 10⁻⁷ m³)/1.29x10⁻⁶ m² = 0.393m
b. the highest possible frequency is given by:
F =
where T= tension, m=mass, L=length
F =
= 297.04/0.786
frequency =377.86Hz