Question

A PVC pipe has a length of 45.132 centimeters.a. What are the frequencies of the first three harmonics when the pipe is open at both ends? Include units in your answers.

Answer 1

Given,

The length of the pipe, L=45.132 cm=0.45132 m

The speed of the sound is v=343 m/s

The frequency of the 1 st harmonic is given by,

$f_1=\frac{v}{2L}$

On substituting the known values,

$\begin{gathered} f_1=\frac{343}{2\times0.45132} \\ =378\text{ Hz} \end{gathered}$

The frequency of the second harmonic is given by,

$f_2=2f_1$

On substituting the known values,

$\begin{gathered} f_2=2\times378 \\ =756\text{ Hz} \end{gathered}$

The frequency of the third harmonic is given by,

$f_3=3f_1$

On substituting the known values,

$\begin{gathered} f_3=3\times378 \\ =1134\text{ Hz} \end{gathered}$

Therefore the frequency of 1st harmonic is 378 Hz.

The frequency of the 2nd harmonic is 765 Hz

The frequency of the 3rd harmonic is 1134 Hz