The vertical displacement of a wave moving along the x-axis is given by$y\left(x,t\right)=\left(0.045\mathrm{m}\right)\cos \left(\left(3.4\mathrm{Hz}\right)t-\left(4.5{\mathrm{m}}^{-1}\right)x\right)$. What is the wave speed and in what direction is it traveling?

Figure 15–44 shows the wave shape at two instants of time for a sinusoidal wave traveling to the right. What is the mathematical representation of this wave?

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

A transverse wave is represented by the following function: $y=\left(18\operatorname{cm}\right)\sin\left[2\pi\left(\frac{x}{2\operatorname{cm}}-\frac{t}{5s}+\frac14\right)\right]$. What is the phase angle of this wave?

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.