Question

A 384 Hz tuning fork is struck over a similar setup to our speed of sound Lab. At what length of column of air would you produce the...1st Harmonic?2nd Harmonic?3rd Harmonic?Justify your answer.Assume the speed of sound in air is 346m/s

Answer 1

We will have the following:

First, we determine the wavelength, that is:

`\begin{gathered} \lambda=(346m/s)/(384Hz)\Rightarrow\lambda=(173)/(192)m \\ \\ \Rightarrow\lambda\approx0.9m \end{gathered}`

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

*1st harmonic:

`\begin{gathered} L=(1)/(2)\lambda\Rightarrow L\approx(1)/(2)(0.9m) \\ \Rightarrow L\approx0.45m \end{gathered}`

So, the first harmonic will be found approximately at 0.45 m.

*2nd harmonic:

`L=(2)/(2)\lambda\Rightarrow L\approx0.9m`

So, the second harmonic will be located at approximately 0.9 m.

*3rd harmonic:

`\begin{gathered} L=(3)/(2)\lambda\Rightarrow L\approx(3)/(2)(0.9m) \\ \\ \Rightarrow L\approx1.35m \end{gathered}`

So, the third harmonic is located at approximately 1.35 m.