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

r = 9.27*10^-4m

Step-by-step 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{(T)/(\mu) }` where
`\mu` is the linear density

`185 = \sqrt{(821)/(\mu) }\\185^(2) = (821)/(\mu) \\\mu = (821)/(185^(2) )\\\mu = 0.024kg/m`

Also;

`\mu` = mass m/Length L

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

`\mu = (\rho V)/(L)`

`\mu = (\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