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?

(II) A transverse wave pulse travels to the right along a string with a speed v = 2.0 m/s. At the shape of the pulse is given by the function D = 0.45 cos (2.6x + 1.2),

where D and x are in meters. (b) Determine a formula for the wave pulse at any time t assuming there are no frictional losses.

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?

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.