Question

An air column which has a fixed length 0.78 m is closed at one end and open at the other end. It produces a 2nd resonant frequency of 335 Hz. Calculate the speed of sound in air.

Answer 1

Perhaps, in the text of the task there is a typo, because there is no second harmonic (or resonant frequency) for a closed-end air column (it produces only odd-numbered harmonics). So, let's assume that air column produces 3rd resonant frequency of 335 Hz. For the third harmonic, the wavelength is $3/4$ the length of closed-end air column. Therefore, we can write:

$$\lambda=\dfrac{3}{4}L=\dfrac{3}{4}\cdot0.78\ m=0.585\ m.$$

Finally, we can find the speed of sound in air from the wave-speed formula:

$$v=f\lambda=335\ Hz\cdot0.585\ m=196\ \dfrac{m}{s}.$$