Standing Waves Video Lessons

Concept

Problem: The wave function of a standing wave is y(x,t)=4.44mmsin[(32.5rad/m)x]sin[(754rad/s)t].Part A: For the two traveling waves that make up this standing wave, find the amplitude.Part B: For the two traveling waves that make up this standing wave, find the wavelength.Part C: For the two traveling waves that make up this standing wave, find the frequency.Part D:  For the two traveling waves that make up this standing wave, find the wave speed.

FREE Expert Solution

The solution of a wave on a string:

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

Part A:

The two waves combine to form a standing wave of amplitude 2A.

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Problem Details

Part A: For the two traveling waves that make up this standing wave, find the amplitude.

Part B: For the two traveling waves that make up this standing wave, find the wavelength.

Part C: For the two traveling waves that make up this standing wave, find the frequency.

Part D:  For the two traveling waves that make up this standing wave, find the wave speed.