Question

A string that is under 54.0 N of tension has linear density 5.20 g/m . A sinusoidal wave with amplitude 2.50 cm and wavelength 1.80 m travels along the string.What is the maximum velocity of a particle on the string?

Answer 1

8.89288275 m/s

Step-by-step explanation:

F = Tension = 54 N

`\mu` = Linear density of string = 5.2 g/m

A = Amplitude = 2.5 cm

Wave velocity is given by

`v=\sqrt{(F)/(\mu)}\\\Rightarrow v=\sqrt{(54)/(5.2* 10^(-3))}\\\Rightarrow v=101.90493\ m/s`

Frequency is given by

`f=(v)/(\lambda)\\\Rightarrow f=(101.90493)/(1.8)\\\Rightarrow f=56.61385\ Hz`

Angular frequency is given by

`\omega=2\pi f\\\Rightarrow \omega=2\pi 56.61385\\\Rightarrow \omega=355.71531\ rad/s`

Maximum velocity of a particle is given by

`v_m=A\omega\\\Rightarrow v_m=0.025* 355.71531\\\Rightarrow v_m=8.89288275\ m/s`

The maximum velocity of a particle on the string is 8.89288275 m/s