Question

A length of nickel wire is subjected to a tension of 821 N. Determine the radius of the wire used if the wave speed of transverse waves moving along this wire is 185 m/s. Take the density of nickel to be 8.90 ✕ 103 kg/m3.

Answer 1

Answer:

r = 9.27*10^-4m

Explanation:

Given the following parameters;

Tension in the wire T = 821N

wave speed of the transverse wave v = 185m/s

density of nickel = 8.9*10³kg/m³

radius of the wire = ?

Using the relationship for finding the speed of the wave to first get the linear density;

$v = \sqrt{\frac{T}{\mu} }$ where $\mu$ is the linear density

$185 = \sqrt{\frac{821}{\mu} }\\185^{2} = \frac{821}{\mu} \\\mu = \frac{821}{185^{2} }\\\mu = 0.024kg/m$

Also;

$\mu$ = mass m/Length L

Since mass m = density $\rho$ * volume $V$

$\mu = \frac{\rho V}{L}$

$\mu = \frac{\rho AL}{L}\\\mu = \rho A$

Since A = area of the wire = $\pi r^{2}$

$\mu = \rho \pi r^{2}$

Given $\mu = 0.024kg/m \ and\ \rho = 8.9*10^{3}kg/m^{3}$

0.024 = 8.9*10³*3.14r²

0.024 = 27.946r²

r² = 0.024/27.964

r² = 8.6*10^-7

r =√8.6*10^-7

r = 9.27*10^-4m

Radius of the wire is 9.27*10^-4m