Question

An air column, open at both ends, has a first harmonic of 330 Hz.a) What are the frequencies of the second and third harmonics?b) If the speed of sound in air is 344 m/s, what is the length of the air column?

Answer 1

Given that the frequency of the first harmonic, f_1 = 330 Hz

We have to find the frequency of the second and third harmonics.

(a) The frequency of the second harmonic is

`\begin{gathered} f_2=2f_1 \\ =2*330 \\ =660\text{ Hz} \end{gathered}`

The frequency of the third harmonic is

`\begin{gathered} f_3=3f_1 \\ =3*330 \\ =990\text{ Hz} \end{gathered}`

(b) The speed of sound in air is v = 344 m/s

Let the length of the air column be l.

The formula to calculate length is

`l_{}=(v)/(2f_1)`

Substituting the values, the length will be

`\begin{gathered} l=(344)/(2*330) \\ =0.521m\text{ } \end{gathered}`