The general equation of a transverse wave is:

$\overline{){\mathbf{y}}{\mathbf{=}}{\mathbf{A}}{\mathbf{s}}{\mathbf{i}}{\mathbf{n}}{\mathbf{(}}{\mathbf{k}}{\mathbf{x}}{\mathbf{+}}{\mathbf{\omega}}{\mathbf{t}}{\mathbf{)}}}$

Speed of the wave:

$\overline{){\mathbf{v}}{\mathbf{=}}\frac{\mathbf{\omega}}{\mathbf{k}}}$

**(a)**

Speed, v = ω/k = 8.65π/0.0246π = 351.6 m/s.

The speed of the wave is 351.6 m/s.

The equation of a transverse wave traveling along a very long string is *y* = 5.43 sin(0.0246*π**x*+ 8.65*π**t*), where *x* and *y* are expressed in centimeters and *t* is in seconds. Determine

**(a)** the speed, **(b)** the direction of propagation of the wave and **(c)** the maximum transverse speed of a particle in the string. **(d)** What is the transverse displacement at *x* = 1.77 cm when *t* = 0.705 s?

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