The Mathematical Description of a Wave Video Lessons

Concept

Problem: A transverse wave on a rope is given by y(x,t)= (0.750cm) cos(π[(0.400cm−1)x+(250s−1)t]).Part A Find the amplitude.Part B Find the period.Part C Find the frequency.Part D Find the wavelength.Part E Find the speed of propagation.Part F Is the wave traveling in the +x- or −x-direction?

FREE Expert Solution

Wave equation:

$\overline{){\mathbf{y}}{\mathbf{\left(}}{\mathbf{x}}{\mathbf{,}}{\mathbf{t}}{\mathbf{\right)}}{\mathbf{=}}{\mathbf{A}}{\mathbf{c}}{\mathbf{o}}{\mathbf{s}}{\mathbf{\left(}}{\mathbf{k}}{\mathbf{x}}{\mathbf{-}}{\mathbf{\omega }}{\mathbf{t}}{\mathbf{\right)}}}$

Expanding the given wave equation:

y(x,t)= 0.750cm cos[π(0.400cm−1)x+π(250s−1)t]

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Problem Details

A transverse wave on a rope is given by y(x,t)= (0.750cm) cos(π[(0.400cm−1)x+(250s−1)t]).

Part A Find the amplitude.

Part B Find the period.

Part C Find the frequency.

Part D Find the wavelength.

Part E Find the speed of propagation.

Part F Is the wave traveling in the +x- or −x-direction?