Question

A guitar string of length L = 0.79 m is oriented along the x-direction and under a tension of T = 74 N. The string is made of steel which has a density of rho = 7800 kg / m3. The radius of the string is r = 8.5 x 10-4 m. A transverse wave of amplitude A = 0.0020 m is formed on the string. Find the string tension.

Answer 1

Answer:

74 N

Explanation:

T = Tension in the string = 74 N

$\rho$ = Density of the steel = 7800 kg/m³

A = Area = $\pi r^2$

r = Radius = $8.5\times 10^{-4}\ m$

Linear density is given by

$\mu=\rho A\\\Rightarrow \mu=7800\times \pi (8.5\times 10^{-4})^2\\\Rightarrow \mu=0.0177\ kg/m$

The linear density is 0.0177 kg/m

Velocity is given by

$v=\sqrt{\dfrac{T}{\mu}}\\\Rightarrow v=\sqrt{\dfrac{74}{0.0177}}\\\Rightarrow v=64.65903\ m/s$

The velocity of the wave on the guitar string is 64.65903 m/s