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

74 N

Step-by-step 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* 10^(-4)\ m`

Linear density is given by

`\mu=\rho A\\\Rightarrow \mu=7800* \pi (8.5* 10^(-4))^2\\\Rightarrow \mu=0.0177\ kg/m`

The linear density is 0.0177 kg/m

Velocity is given by

`v=\sqrt{(T)/(\mu)}\\\Rightarrow v=\sqrt{(74)/(0.0177)}\\\Rightarrow v=64.65903\ m/s`

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