# 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

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Waves on a String concept. You can view video lessons to learn Waves on a String. Or if you need more Waves on a String practice, you can also practice Waves on a String practice problems.