Light has both a wave and a particle nature. Particles have a wave nature as well, and therefore which of the following statements is correct about particles such as $electrons$?

Write the mathematical representation of the wave graphed in the following two figures.

The function for some transverse wave is ? = (0.5 m) sin [(0.8 m⁻¹)x − 2?(50 Hz)t + π/3]. What is the transverse velocity at t=2 s, x=7 cm? What is the maximum transverse speed? The maximum transverse acceleration?

A transverse harmonic wave moving to the left has a wavelength of 2.5 m and a wave speed of 12 m/s. The amplitude of the wave is 0.1 m. At x = 0 and t = 0, the displacement of the wave is y = 0. Write the wave function for this wave.

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is $y(x,t)=\(\left\)(2.30\(\operatorname{mm)}\]\cos\)[\(\left\)(16.98\(\text{ }\)rad/m\(\right\))x+(742\(\text{ }\)rad/s\(\right\))t]$. Being more practical, you measure the rope to have a length of $1.35\(\text{ m}\)$ and a mass of $0.00338\(\operatorname{kg}\)$. You are then asked to determine the following: (d) wave speed; (e) direction the wave is traveling;