Problem: 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/sdirection_________(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

FREE Expert Solution

Wave function is expressed as:

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

(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.

Problem Details

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