A platinum wire that is 1.20 m long has a radius of 0.500 mm and is fixed at both ends. In its third harmonic it vibrates at 512 Hz. The density of platinum is 21.4 × 10³ kg/m³. What is the tension in the wire? A) 4.00 kN B) 2.00 kN C) 2.82 kN D) 1.41 kN E) 1.00 kN

Question

Quizplus · Accepted Answer

The frequency of the third harmonic is given by:
f = (3v)/(2L)
where v is the speed of sound in the wire and L is its length.
Rearranging, we have:
v = (2Lf)/3
The speed of sound in a wire is given by:
v = sqrt(T/µ)
where T is the tension in the wire and µ is its linear density (mass per unit length).
Rearranging, we have:
T = µv^2
Substituting the expressions for v and µ, we get:
T = (4L^2f^2µ)/9
Substituting the given values, we get:
T = (4 x (1.20 m)^2 x (512 Hz)^2 x 21.4 x 10^3 kg/m) / 9
T = 2820 N = 2.82 kN (to three significant figures)
Therefore, the best choice is C, which gives the correct tension in the wire.

A Platinum Wire That Is 1