Question

A string is stretched from end to end oscillating at a frequency of 120 Hz. If the speed of sound on thestring is 80.9m/s, where should I put my finger (node) to create standing waves for the...1st Harmonic?2nd Harmonic?3rd Harmonic?Justify your answer.

Answer 1

We will have the following:

First, we determine the wave length, that is:

$\begin{gathered} \lambda=\frac{v}{f} \\ \\ \Rightarrow\lambda=\frac{80.9m/s}{120Hz}\Rightarrow\lambda=\frac{809}{1200}m \\ \Rightarrow\lambda=0.6741666666...m\Rightarrow\lambda\approx0.67m \end{gathered}$

So, the wave length is approximately 0.67 meters.

Now, we determine the 1st, 2nd and 3rd harmonics, that is:

*1st harmonic:

$\begin{gathered} L=\frac{1}{2}\lambda\Rightarrow L\approx\frac{1}{2}(0.67m) \\ \\ \Rightarrow L\approx0.335m \end{gathered}$

So, the first harmonic is at approximately 0.335 m.

*2nd harmonic:

$L=\frac{2}{2}\lambda\Rightarrow L\approx0.67m$

So, the second harmonic is located at approximately 0.67m.

*3rd harmonic:

$\begin{gathered} L=\frac{3}{2}\lambda\Rightarrow L\approx\frac{3}{2}(0.67m) \\ \Rightarrow L\approx1.005m \end{gathered}$

So, the third harmonic is located at approximately 1.005 m.