A string or rope will break apart if it is placed under too much tensile stress [Tensile stress = 
]. Thicker ropes can withstand more tension without breaking because the thicker the rope, the greater the cross-sectional area and the smaller the stress. One type of steel has density 7800 kg/m 3 and will break if the tensile stress exceeds 7.0 × 10 8 N/m 2 . You want to make a guitar string from 4.0 g of this type of steel. In use, the guitar string must be able to withstand a tension of 900 N without breaking. Your job is the following:
Text Solution
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The breaking stress is 
= 7.0 × 10 8 N/m 2 , and the maximum tension is F = 900 N,
so solving for r gives the minimum radius
r = 
= 6.4 × 10 –4 m.
The mass and density are fixed, ρ = 
,
so the minimum radius gives the maximum length L = 
= 
=0.40m
( b) The fundamental frequency is f 1
= 
= 
= 
.
Assuming the maximum length of the string is free to vibrate, the highest fundamental frequency occurs when
F = 900 N, f 1 = 
= 376 Hz.
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