Standing Waves Video Lessons

Concept

# Problem: The figure shows a standing wave on a string.Draw the standing wave that occurs if the string tension is quadrupled while the frequency is held constant.

###### FREE Expert Solution

Frequency of oscillation for a stretched string:

$\overline{){\mathbf{f}}{\mathbf{=}}\frac{\mathbf{n}}{\mathbf{2}\mathbf{L}}{\mathbf{·}}\sqrt{\frac{\mathbf{T}}{\mathbf{\mu }}}}$

Solving for n:

$\overline{){\mathbf{n}}{\mathbf{=}}{\mathbf{2}}{\mathbf{L}}{\mathbf{f}}{\mathbf{·}}\sqrt{\frac{\mathbf{\mu }}{\mathbf{T}}}}$

We have the initial nodes, ni = 2 and initial tension, Ti.

The final tension is 4Ti.

We'll solve for new nodes, nfinal, as follows:

${\mathbit{n}}_{\mathbf{i}}\mathbf{=}\mathbf{2}\mathbit{L}{\mathbit{f}}_{\mathbf{1}}\mathbf{·}\sqrt{\frac{\mathbf{\mu }}{{\mathbf{T}}_{\mathbf{i}}}}$

${\mathbit{n}}_{\mathbf{f}}\mathbf{=}\mathbf{2}\mathbit{L}{\mathbit{f}}_{\mathbf{1}}\mathbf{·}\sqrt{\frac{\mathbf{\mu }}{\mathbf{4}{\mathbf{T}}_{\mathbf{i}}}}$

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###### Problem Details

The figure shows a standing wave on a string.

Draw the standing wave that occurs if the string tension is quadrupled while the frequency is held constant.

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

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