A tuning fork with a frequency of 440 Hz is connected to a long...

Given:
Frequency of the tuning fork, $f = 440 \text{ Hz}$
Amplitude of the transverse wave, $A = 0.50 \text{ mm} = 0.50 \times 10^{-3} \text{ m}$

The angular frequency of the wave is:
$\omega = 2\pi f = 2\pi \times 440 = 880\pi \text{ rad s}^{-1}$

The maximum speed of a particle on the string is given by:
v_{\text\max} = A\omega
v_{\text\max} = (0.50 \times 10^{-3} \text{ m}) \times (880\pi \text{ rad s}^{-1}) = 0.44\pi \text{ m s}^{-1}
v_{\text\max} \approx 1.38 \text{ m s}^{-1} \approx 1.4 \text{ m s}^{-1}

The maximum acceleration of a particle on the string is given by:
a_{\text\max} = A\omega^2
a_{\text\max} = v_{\text\max}\omega = 0.44\pi \times 880\pi \approx 3824 \text{ m s}^{-2}
a_{\text\max} \approx 3.8 \text{ km s}^{-2}

The values of tension and linear mass density are not required to find the maximum speed and acceleration of the particle.