Frequency of oscillation for a stretched string:

$\overline{){\mathbf{f}}{\mathbf{=}}\frac{\mathbf{n}}{\mathbf{2}\mathbf{L}}{\mathbf{\xb7}}\sqrt{\frac{\mathbf{T}}{\mathbf{\mu}}}}$

Solving for n:

$\overline{){\mathbf{n}}{\mathbf{=}}{\mathbf{2}}{\mathbf{L}}{\mathbf{f}}{\mathbf{\xb7}}\sqrt{\frac{\mathbf{\mu}}{\mathbf{T}}}}$

We have the initial nodes, n_{i} = 2 and initial tension, T_{i}.

The final tension is 4T_{i}.

We'll solve for new nodes, n_{final}, as follows:

${\mathit{n}}_{\mathbf{i}}\mathbf{=}\mathbf{2}\mathit{L}{\mathit{f}}_{\mathbf{1}}\mathbf{\xb7}\sqrt{\frac{\mathbf{\mu}}{{\mathbf{T}}_{\mathbf{i}}}}$

${\mathit{n}}_{\mathbf{f}}\mathbf{=}\mathbf{2}\mathit{L}{\mathit{f}}_{\mathbf{1}}\mathbf{\xb7}\sqrt{\frac{\mathbf{\mu}}{\mathbf{4}{\mathbf{T}}_{\mathbf{i}}}}$

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.

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 Standing Waves concept. You can view video lessons to learn Standing Waves. Or if you need more Standing Waves practice, you can also practice Standing Waves practice problems.