Answer:
8.89288275 m/s
Explanation:
F = Tension = 54 N
[tex]\mu[/tex] = Linear density of string = 5.2 g/m
A = Amplitude = 2.5 cm
Wave velocity is given by
[tex]v=\sqrt{\frac{F}{\mu}}\\\Rightarrow v=\sqrt{\frac{54}{5.2\times 10^{-3}}}\\\Rightarrow v=101.90493\ m/s[/tex]
Frequency is given by
[tex]f=\frac{v}{\lambda}\\\Rightarrow f=\frac{101.90493}{1.8}\\\Rightarrow f=56.61385\ Hz[/tex]
Angular frequency is given by
[tex]\omega=2\pi f\\\Rightarrow \omega=2\pi 56.61385\\\Rightarrow \omega=355.71531\ rad/s[/tex]
Maximum velocity of a particle is given by
[tex]v_m=A\omega\\\Rightarrow v_m=0.025\times 355.71531\\\Rightarrow v_m=8.89288275\ m/s[/tex]
The maximum velocity of a particle on the string is 8.89288275 m/s
