To solve this problem it is necessary to apply the concepts related to frequency as a function of speed and wavelength as well as the kinematic equations of simple harmonic motion
From the definition we know that the frequency can be expressed as
[tex]f = \frac{v}{\lambda}[/tex]
Where,
[tex]v = Velocity \rightarrow 20m/s[/tex]
[tex]\lambda = Wavelength \rightarrow 35*10^{-2}m[/tex]
Therefore the frequency would be given as
[tex]f = \frac{20}{35*10^{-2}}[/tex]
[tex]f = 57.14Hz[/tex]
The frequency is directly proportional to the angular velocity therefore
[tex]\omega = 2\pi f[/tex]
[tex]\omega = 2\pi *57.14[/tex]
[tex]\omega = 359.03rad/s[/tex]
Now the maximum speed from the simple harmonic movement is given by
[tex]V_{max} = A\omega[/tex]
Where
A = Amplitude
Then replacing,
[tex]V_{max} = (1*10^{-2})(359.03)[/tex]
[tex]V_{max} = 3.59m/s[/tex]
Therefore the maximum speed of a point on the string is 3.59m/s
