Wave function is expressed as:

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

**(a)**

Speed of a wave is:

v = ω/k = 14π/2π = 7 m/s and is in positive x-direction.

The speed and direction of travel of the wave is 7 m/s in the positive x-direction.

The wave function for a traveling wave on a taut string is (in SI units)

y(x,t) = 0.375 sin (14πt - 2πx + π/4)

(a) What are the speed and direction of travel of the wave?

speed _____ m/s

direction_________

(positive x-direction, positive y-direction, positive z-direction, negative x-direction, negative y-direction, negative z-direction)

(b) What is the vertical position of an element of the string at t = 0, x = 0.178 m?

________m

(c) What is the wavelength of the wave?

____________m

(d) What is the frequency of the wave?

________ Hz

(e) What is the maximum transverse speed of an element of the string?

_____ m/s

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